Empirical density estimation

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Empirical density estimation

Bogaso
Hi,

Let say I have below vector of data-points :

Dat = c(-0.444444444444444, -0.25, -0.237449799196787, -0.227467046669042,

-0.227454464682363, -0.22, -0.214876033057851, -0.211781206171108,

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-0.024390243902439, -0.0241935483870968, -0.0238907849829351,

-0.0238153295944078, -0.0234413496961306, -0.0232558139534884,

-0.0232558139534883, -0.0230392156862745, -0.0230360307147077,

-0.0228847365106026, -0.0225806451612903, -0.0224519940915805,

-0.0214786344110332, -0.0212360867018161, -0.0205245153933865,

-0.0204170602339606, -0.0200986321764215, -0.0200729927007299,

-0.0199828473413379, -0.0194174757281553, -0.0193536931818183,

-0.0192885771543086, -0.019222732971166, -0.0191414840759143,

-0.0189573459715641, -0.0188902007083826, -0.0186903321231681,

-0.0184456468273487, -0.0183066361556064, -0.0182166826462128,

-0.0181149908112366, -0.0179372197309418, -0.0179172441100772,

-0.0178571428571429, -0.0174672489082969, -0.0174216027874564,

-0.0171428571428572, -0.017017253604349, -0.0169252468265163,

-0.0165094339622642, -0.0158730158730158, -0.0158415841584159,

-0.0157247037374659, -0.0157089706490286, -0.0156250000000001,

-0.0153846153846153, -0.0151668351870576, -0.0151589242053789,

-0.0150489089541008, -0.0150262202501008, -0.0150081124932396,

-0.0148196281468128, -0.0144251166737377, -0.0142857142857142,

-0.0140638734251392, -0.0136986301369863, -0.0133333333333333,

-0.0129464285714286, -0.0129449838187702, -0.0127813811522321,

-0.0126030053320408, -0.0125721665147373, -0.0125, -0.0122160435399906,

-0.0122116689280869, -0.0121019108280255, -0.0118747750989563,

-0.0118277953189996, -0.0117107942973524, -0.0115172759138707,

-0.0114087997381585, -0.0113924050632912, -0.0111524163568772,

-0.0111248454882571, -0.0111111111111111, -0.0102570933795125,

-0.0102040816326532, -0.00963463463463469, -0.00958657878969439,

-0.00941028858218319, -0.00874453466583389, -0.00779588944011335,

-0.00713620850139625, -0.00710720027075056, -0.00709219858156026,

-0.00624999999999998, -0.00551977920883173, -0.00521499557217353,

-0.00453998797354176, -0.00444444444444444, -0.00166389351081533,

-0.00118483412322285, -0.00100704934541787, -0.000937500000000036,

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,

0.000218031178458569, 0.000796495420151402, 0.00167130919220062,

0.00190476190476193, 0.00350058343057173, 0.00363914958820145,

0.00432900432900424, 0.00456037942356804, 0.00477446915441642,

0.0050825509873745, 0.00525691029336935, 0.00603318250377083,

0.00652173913043472, 0.00733192494097176, 0.00747663551401869,

0.00760456273764256, 0.00812529439472442, 0.00991231414410967,

0.0101685066821615, 0.0106182565507793, 0.0109070034443169, 0.0115183246073298,

0.0115442244823827, 0.0127659574468085, 0.0128076846107665, 0.0135135135135135,

0.0140845070422535, 0.0150730098916627, 0.0159362549800796, 0.0172413793103449,

0.0176899063475547, 0.0186954715413378, 0.0187765706188003, 0.0195757403189066,

0.019607843137255, 0.0199999999999999, 0.0210526315789473, 0.0221979621542939,

0.0239410681399632, 0.0239999999999999, 0.025149051490515, 0.0260869565217392,

0.0262475696694749, 0.028180542563143, 0.0285714285714286, 0.0303030303030302,

0.0315904139433552, 0.0341864716636198, 0.0375782881002089, 0.038479809976247,

0.0387596899224806, 0.0416666666666667, 0.0428100987925357, 0.0428134556574923,

0.0437201907790144, 0.0451127819548872, 0.0460251046025105, 0.0487779511180447,

0.048975188781014, 0.0529872938632063, 0.0562390158172233, 0.0589335827876521,

0.0617551462621885, 0.0628115653040877, 0.0671812464265294, 0.0721784776902887,

0.0736842105263157, 0.0833333333333334, 0.083862394802894, 0.0970464135021097,

0.0971168437025795, 0.102272727272727, 0.111111111111111, 0.117117117117117,

0.123532699832309, 0.141304347826087, 0.179487179487179, 0.191268191268191,

0.205128205128205, 0.219020172910663, 0.271590909090909, 0.333333333333333

)


Now I want to estimate empirical PDF for interval of (-1, 1) including
all points of Dat

I have looked into the density() function, however it appears that,
empirical density is estimated for equally distant points, which not
necessarily contains actual supplied points (in my case, Dat)

Is there any option to achieve the same?

Thanks for your pointer.

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Re: Empirical density estimation

Bert Gunter-2
You need to re-read ?density and perhaps think again -- or do some study --
about how a (kernel) density estimate works. The points at which the
estimate is calculated are *not* the values given, nor should they be!

Cheers,
Bert



Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Sun, Mar 11, 2018 at 11:45 AM, Christofer Bogaso <
[hidden email]> wrote:

> Hi,
>
> Let say I have below vector of data-points :
>
> Dat = c(-0.444444444444444, -0.25, -0.237449799196787, -0.227467046669042,
>
> -0.227454464682363, -0.22, -0.214876033057851, -0.211781206171108,
>
> -0.199891067538126, -0.192920353982301, -0.192307692307692,
> -0.186046511627907,
>
> -0.184418145956608, -0.181818181818182, -0.181818181818182,
> -0.181266261925412,
>
> -0.181003118503119, -0.179064587973274, -0.178217821782178,
> -0.17809021675454,
>
> -0.177685950413223, -0.177570093457944, -0.176470588235294,
> -0.176470588235294,
>
> -0.174825741611282, -0.168021680216802, -0.166666666666667,
> -0.166666666666667,
>
> -0.166380789022298, -0.164209115281501, -0.164011246485473,
> -0.162689804772234,
>
> -0.162361623616236, -0.160161507402423, -0.16, -0.155038759689922,
>
> -0.154172560113154, -0.15311004784689, -0.151515151515152,
> -0.151462994836489,
>
> -0.151098901098901, -0.150537634408602, -0.150442477876106,
> -0.150406504065041,
>
> -0.149904214559387, -0.149882903981265, -0.149797570850202,
> -0.148496240601504,
>
> -0.148325358851675, -0.147540983606557, -0.147239263803681,
> -0.146989966555184,
>
> -0.14622641509434, -0.146095717884131, -0.145994832041344,
> -0.14572864321608,
>
> -0.145161290322581, -0.144292237442922, -0.144144144144144,
> -0.144021739130435,
>
> -0.14375, -0.142212189616253, -0.141122913505311, -0.140324963072378,
>
> -0.139344262295082, -0.13884007029877, -0.138356164383562,
> -0.137626262626263,
>
> -0.137142857142857, -0.136690647482014, -0.136577708006279,
> -0.136363636363636,
>
> -0.136094674556213, -0.135879774577332, -0.135586319218241,
> -0.135135135135135,
>
> -0.132780082987552, -0.132209405501331, -0.132023755139333,
> -0.131233595800525,
>
> -0.130434782608696, -0.130434782608696, -0.130268199233717,
> -0.128813559322034,
>
> -0.1284046692607, -0.128205128205128, -0.128182616330114,
> -0.127937336814621,
>
> -0.126283367556468, -0.125853658536585, -0.125448028673835,
> -0.125425564840607,
>
> -0.125311203319502, -0.125, -0.124401913875598, -0.124248496993988,
>
> -0.124031007751938, -0.123572170301142, -0.123188405797102,
> -0.122905027932961,
>
> -0.121666666666667, -0.121573685907772, -0.120658135283364,
> -0.120540019286403,
>
> -0.119858156028369, -0.11965811965812, -0.11965811965812,
> -0.119565217391304,
>
> -0.118942731277533, -0.117820324005891, -0.116257947320618,
> -0.115789473684211,
>
> -0.115683584819387, -0.115384615384615, -0.115281501340483,
> -0.114492753623188,
>
> -0.114357262103506, -0.114285714285714, -0.114035087719298,
> -0.113181972212809,
>
> -0.112790697674419, -0.112781954887218, -0.112195121951219,
> -0.112191473448018,
>
> -0.111111111111111, -0.111111111111111, -0.110813226094727,
> -0.110384300899428,
>
> -0.110147441457069, -0.110137672090113, -0.109913793103448,
> -0.109792284866469,
>
> -0.109375, -0.10919540229885, -0.109112709832134, -0.10844250363901,
>
> -0.107776617954071, -0.10752688172043, -0.107317073170732,
> -0.106674272675414,
>
> -0.106382978723404, -0.106100795755968, -0.106060606060606,
> -0.10595160235448,
>
> -0.105742474070326, -0.105263157894737, -0.104454685099846,
> -0.104283054003724,
>
> -0.103916449086162, -0.103723404255319, -0.103448275862069,
> -0.102737680438029,
>
> -0.10267471958585, -0.101696871753434, -0.100893997445721,
> -0.10041265474553,
>
> -0.100042983021706, -0.1, -0.0995111731843576, -0.099502487562189,
>
> -0.0994117647058824, -0.0991561181434598, -0.0989492119089317,
>
> -0.0988372093023255, -0.0983908045977012, -0.0983050847457627,
>
> -0.0977198697068404, -0.0974702380952382, -0.0973819695475956,
>
> -0.097345132743363, -0.0971472629144179, -0.0971438645980254,
>
> -0.0961538461538461, -0.096062667491239, -0.0957347238935687,
>
> -0.0956521739130435, -0.0954773869346733, -0.0954115076474873,
>
> -0.0952380952380952, -0.0951115834218915, -0.0950642007303569,
>
> -0.0949423247559894, -0.0947368421052631, -0.0946291560102303,
>
> -0.0945220193340494, -0.0944309927360775, -0.0943016759776536,
>
> -0.0942720763723149, -0.0941770647653002, -0.0940298507462686,
>
> -0.094017094017094, -0.0935672514619884, -0.0934579439252337,
>
> -0.0930232558139535, -0.0929772502472798, -0.0929054054054054,
>
> -0.0928778745255637, -0.0927700348432055, -0.0925266903914591,
>
> -0.0922502666192677, -0.0918094218415418, -0.0915254237288135,
>
> -0.0914774596906876, -0.0914662894860915, -0.0914285714285715,
>
> -0.0912322274881517, -0.090909090909091, -0.0909090909090909,
>
> -0.09079754601227, -0.0907071455016661, -0.0906593406593406,
>
> -0.0903614457831325, -0.0903323548906352, -0.09, -0.0897243107769424,
>
> -0.0896358543417368, -0.0895522388059702, -0.0895052902487847,
>
> -0.0891719745222929, -0.0888888888888888, -0.0887227819304518,
>
> -0.0887096774193548, -0.0886956521739131, -0.0884703196347032,
>
> -0.0884450784593437, -0.0884413309982488, -0.0883577310155536,
>
> -0.0883054892601431, -0.0882917466410749, -0.0881628999776236,
>
> -0.0881193929739248, -0.0880681818181819, -0.0878186968838525,
>
> -0.087719298245614, -0.0876010781671159, -0.0873634945397815,
>
> -0.0872641509433961, -0.0871512228728901, -0.0871032050299035,
>
> -0.0868133772309825, -0.0865384615384615, -0.0858895705521473,
>
> -0.085742525327403, -0.0855766209280403, -0.0854700854700855,
>
> -0.0853994490358125, -0.0853658536585365, -0.0851063829787235,
>
> -0.085048426150121, -0.0849673202614379, -0.084862385321101,
>
> -0.0843335637529065, -0.0843222985633979, -0.084315503173164,
>
> -0.0842105263157896, -0.0841423948220064, -0.0838323353293414,
>
> -0.0836501901140684, -0.083422459893048, -0.0833333333333334,
>
> -0.0833333333333333, -0.0827236916150815, -0.0826723611958512,
>
> -0.0826039387308535, -0.0824242424242424, -0.0821513002364065,
>
> -0.0820932539682539, -0.0820713238886174, -0.0818181818181818,
>
> -0.0816618911174786, -0.0816613868356214, -0.0816326530612244,
>
> -0.081619937694704, -0.0813748531139835, -0.0811965811965812,
>
> -0.0810372771474878, -0.0809095716552088, -0.0808823529411764,
>
> -0.0808414831492295, -0.0807511737089201, -0.0805722891566266,
>
> -0.0803474484256242, -0.0800000000000001, -0.0800000000000001,
>
> -0.0799584631360333, -0.0795941847087125, -0.0795930580490723,
>
> -0.0794701986754966, -0.0793650793650794, -0.0791855203619909,
>
> -0.0790273556231002, -0.0790273556231002, -0.0789473684210527,
>
> -0.0789473684210526, -0.0787545787545788, -0.0787461773700307,
>
> -0.0786724031960664, -0.0782122905027933, -0.078177727784027,
>
> -0.078125, -0.0778443113772455, -0.0776310524209684, -0.0775862068965517,
>
> -0.0775577557755776, -0.0773930753564156, -0.0772686433063791,
>
> -0.0771513353115727, -0.0771200000000001, -0.0770370370370371,
>
> -0.076923076923077, -0.076923076923077, -0.0769039940461424,
>
> -0.076592082616179, -0.0763425253991292, -0.0762886597938145,
>
> -0.0762886597938145, -0.0761565836298932, -0.0760869565217391,
>
> -0.07597645799893, -0.0758377425044092, -0.0757314974182444,
>
> -0.0755148741418765, -0.0754814305364511, -0.0754189944134078,
>
> -0.0752351097178683, -0.0750988142292491, -0.074935400516796,
>
> -0.0748663101604277, -0.0748031496062992, -0.0747663551401868,
>
> -0.0747295968534907, -0.0747028862478777, -0.0745967741935485,
>
> -0.0741784037558686, -0.0740740740740741, -0.0740740740740741,
>
> -0.0740740740740741, -0.073828125, -0.0736698499317872,
> -0.0735877862595421,
>
> -0.0735824009102977, -0.0735632183908046, -0.0733944954128441,
>
> -0.0728862973760932, -0.0728279386712096, -0.0726480203414457,
>
> -0.0726329442282749, -0.072632190586868, -0.0725766664070006,
>
> -0.0724137931034483, -0.0722664432341852, -0.0719257540603249,
>
> -0.0717538461538461, -0.0716612377850163, -0.0715181932245923,
>
> -0.0714285714285715, -0.0714285714285713, -0.0710646285867525,
>
> -0.0708446866485014, -0.0708117443868739, -0.0708028321132845,
>
> -0.0706436420722135, -0.0705325930495579, -0.0705128205128205,
>
> -0.0705009276437847, -0.0704043019318861, -0.0702106318956871,
>
> -0.0701663201663202, -0.0700661736084078, -0.0699999999999999,
>
> -0.0695540857691487, -0.0692979983084297, -0.0691823899371069,
>
> -0.0691244239631336, -0.0690335305719921, -0.0689655172413792,
>
> -0.0688536409516944, -0.068450039339103, -0.0682332955832389,
>
> -0.0682261208576998, -0.0681818181818182, -0.0679035250463822,
>
> -0.0679012345679012, -0.0677966101694916, -0.0676384839650145,
>
> -0.0675675675675676, -0.0675241157556271, -0.067463706233988,
>
> -0.0674584323040379, -0.0668523676880222, -0.0666666666666667,
>
> -0.066526455612132, -0.0664206642066421, -0.066321243523316,
>
> -0.0662949194547709, -0.0662579580287669, -0.0662251655629139,
>
> -0.0661764705882353, -0.0661478599221789, -0.0657894736842105,
>
> -0.0657534246575342, -0.0654481924472518, -0.0652900974262034,
>
> -0.0652225100070638, -0.0651126106388572, -0.0650887573964497,
>
> -0.0650684931506849, -0.0650195058517555, -0.0649954627949184,
>
> -0.0649081209247184, -0.064891846921797, -0.0648899188876013,
>
> -0.0648148148148149, -0.0645962732919255, -0.0644599303135888,
>
> -0.0644171779141105, -0.0643564356435644, -0.064327485380117,
>
> -0.0642667310944672, -0.0641975308641976, -0.0641025641025641,
>
> -0.0639197041732701, -0.0638436482084691, -0.0635245901639343,
>
> -0.0634996041171813, -0.0632017594629008, -0.0631313131313131,
>
> -0.0630434782608695, -0.0629405840886203, -0.0629155024568842,
>
> -0.0628765060240964, -0.0628571428571429, -0.0625394819962098,
>
> -0.062476757158795, -0.06203552416592, -0.0620347394540943,
> -0.0619971604354,
>
> -0.0619946091644204, -0.0619469026548672, -0.0619235836627141,
>
> -0.0618131868131868, -0.0617667356797793, -0.0617312601531677,
>
> -0.0616740088105726, -0.0614161849710983, -0.0613026819923372,
>
> -0.0612244897959185, -0.0610859728506788, -0.0610526315789473,
>
> -0.0610399397136398, -0.0610169491525424, -0.0609659540775929,
>
> -0.0608695652173912, -0.0606060606060606, -0.0606060606060606,
>
> -0.0604929051530994, -0.0604204204204204, -0.0603636363636364,
>
> -0.0602698650674663, -0.0602115541090318, -0.0599352051835853,
>
> -0.0599001663893511, -0.0596379126730565, -0.0594227504244482,
>
> -0.0587275693311581, -0.0587002096436059, -0.0586319218241041,
>
> -0.0586046511627907, -0.0584174190122145, -0.0584011488750599,
>
> -0.0583707504810776, -0.0579299691040165, -0.0579268292682926,
>
> -0.0579050097592712, -0.057608079558922, -0.0574712643678161,
>
> -0.0572450805008944, -0.0570958904109589, -0.0568263045032167,
>
> -0.0568181818181818, -0.0568181818181818, -0.0568031704095112,
>
> -0.0566301923974486, -0.0566037735849057, -0.0566037735849057,
>
> -0.0566037735849056, -0.0564433866031963, -0.0562770562770562,
>
> -0.0561576354679803, -0.0560928433268858, -0.0559006211180124,
>
> -0.0558213716108453, -0.055689240288759, -0.0554101893181468,
>
> -0.0553961597881263, -0.0553633217993079, -0.0553571428571429,
>
> -0.0553481577665964, -0.0553158101216163, -0.0553108174253549,
>
> -0.0548340548340548, -0.0546601261387525, -0.054590570719603,
>
> -0.0545001187366422, -0.0544511668107173, -0.0544274300932089,
>
> -0.0542372881355932, -0.0542168674698794, -0.0540540540540541,
>
> -0.053763440860215, -0.0537513997760358, -0.0536343468615424,
>
> -0.0535714285714286, -0.0534725518114223, -0.0529294274300931,
>
> -0.0528846153846155, -0.0528756957328386, -0.0526458340386634,
>
> -0.0526315789473684, -0.0525606469002696, -0.0525451559934318,
>
> -0.0525227460711332, -0.051948051948052, -0.051792828685259,
>
> -0.0517241379310345, -0.0513784461152881, -0.0513559322033898,
>
> -0.0512610211195407, -0.0512437810945274, -0.051150895140665,
>
> -0.0510695486616643, -0.0507726269315673, -0.0507377685736475,
>
> -0.0506575742815391, -0.0506024096385543, -0.0505494505494506,
>
> -0.0503194888178913, -0.0501567398119122, -0.05, -0.0499001996007984,
>
> -0.0498214285714285, -0.0497737556561087, -0.0497470489038785,
>
> -0.0494845360824741, -0.0493827160493827, -0.0492157923201731,
>
> -0.0491192897035657, -0.0489642184557439, -0.0488200324265898,
>
> -0.0488031366075114, -0.0485151426051161, -0.0483319076133448,
>
> -0.0481220657276996, -0.0480897675661234, -0.0480599647266314,
>
> -0.0480038022813688, -0.0479900280461202, -0.0479548660084627,
>
> -0.0478449164776243, -0.0475638051044084, -0.0475342709631477,
>
> -0.0473213579172271, -0.0472997462848857, -0.0472050636772667,
>
> -0.046890780551147, -0.0467625899280576, -0.046753107010276,
>
> -0.0466592011944754, -0.0465772759350741, -0.0465753424657535,
>
> -0.0464333781965007, -0.0463888365076373, -0.0463215258855587,
>
> -0.046281851274051, -0.0459946060208471, -0.0458715596330275,
>
> -0.0458563535911603, -0.0457367549668873, -0.0456500165398611,
>
> -0.0454373701114679, -0.0454265548766046, -0.0454183266932271,
>
> -0.045213508233324, -0.045182571340902, -0.0451018428709989,
>
> -0.0451018428709989, -0.044955044955045, -0.0444136016655101,
>
> -0.0443722943722945, -0.0442996742671011, -0.0442477876106195,
>
> -0.0442477876106195, -0.0441176470588236, -0.043982895540623,
>
> -0.0438184663536776, -0.0436363636363636, -0.043261231281198,
>
> -0.0432218514782339, -0.0431654676258993, -0.0424336600525938,
>
> -0.0423429781227946, -0.0423387096774193, -0.0420711974110032,
>
> -0.0420083118050095, -0.0420032310177707, -0.0417256011315418,
>
> -0.0416842105263158, -0.0416141235813367, -0.0414593698175788,
>
> -0.0413793103448276, -0.041320942582144, -0.0407865986890023,
>
> -0.0406158747013539, -0.0405803571428572, -0.0405643738977073,
>
> -0.040422053796998, -0.040268456375839, -0.0400500625782228,
>
> -0.0400449101796407, -0.04, -0.0399718147460123, -0.0399137001078749,
>
> -0.0399044464954666, -0.0398863290368415, -0.0398230088495575,
>
> -0.0394736842105263, -0.0393401015228426, -0.0392720306513411,
>
> -0.0392156862745098, -0.0388349514563106, -0.0386904761904763,
>
> -0.0384615384615385, -0.0382457345700217, -0.0382293762575454,
>
> -0.0381840048105834, -0.0380030474141795, -0.0379746835443038,
>
> -0.0379247280777747, -0.0376432078559739, -0.0375494071146245,
>
> -0.0375490837696336, -0.0373345788572318, -0.0372940156114484,
>
> -0.0371871275327772, -0.037037037037037, -0.0368133174791915,
>
> -0.0368098159509203, -0.0367231638418078, -0.0361445783132531,
>
> -0.0360915492957746, -0.0357142857142857, -0.0356663184599313,
>
> -0.0356413696552528, -0.035513103110458, -0.0353194103194103,
>
> -0.0352112676056338, -0.0350119904076739, -0.0349794238683129,
>
> -0.0349373764007909, -0.0349091600875106, -0.0347826086956522,
>
> -0.0347728547392037, -0.0347682119205298, -0.0346083788706739,
>
> -0.0344706296166022, -0.0344421548425081, -0.0341176470588236,
>
> -0.0338983050847458, -0.033457249070632, -0.0334208223972004,
>
> -0.0333333333333334, -0.0333333333333333, -0.0329670329670331,
>
> -0.0329144225014961, -0.0326797385620915, -0.0323033707865168,
>
> -0.0322118826055834, -0.0321750321750322, -0.0320890635232481,
>
> -0.0318302387267905, -0.0316666666666666, -0.0315586914688903,
>
> -0.0312606184165817, -0.030881017257039, -0.0308764940239045,
>
> -0.0305419952434597, -0.030406198638178, -0.0299651567944252,
>
> -0.029945999018164, -0.0298786181139121, -0.0295741147960329,
>
> -0.0293917033546227, -0.029171528588098, -0.0291327913279132,
>
> -0.0290497291974397, -0.0288721376760064, -0.0287704170466792,
>
> -0.0286236297198539, -0.0285714285714286, -0.0277575837684224,
>
> -0.0277085471338513, -0.0275897304892068, -0.0275526742301458,
>
> -0.027027027027027, -0.0270270270270269, -0.0269087523277468,
>
> -0.0268918695148203, -0.02676704307821, -0.026454253142356,
> -0.0263157894736842,
>
> -0.0263157894736842, -0.0261660978384529, -0.025974025974026,
>
> -0.0257503107796129, -0.0255319148936171, -0.0254237288135594,
>
> -0.025297619047619, -0.0249174422095467, -0.0248888888888889,
>
> -0.024767619719967, -0.0246053853296194, -0.0245269796776454,
>
> -0.024390243902439, -0.0241935483870968, -0.0238907849829351,
>
> -0.0238153295944078, -0.0234413496961306, -0.0232558139534884,
>
> -0.0232558139534883, -0.0230392156862745, -0.0230360307147077,
>
> -0.0228847365106026, -0.0225806451612903, -0.0224519940915805,
>
> -0.0214786344110332, -0.0212360867018161, -0.0205245153933865,
>
> -0.0204170602339606, -0.0200986321764215, -0.0200729927007299,
>
> -0.0199828473413379, -0.0194174757281553, -0.0193536931818183,
>
> -0.0192885771543086, -0.019222732971166, -0.0191414840759143,
>
> -0.0189573459715641, -0.0188902007083826, -0.0186903321231681,
>
> -0.0184456468273487, -0.0183066361556064, -0.0182166826462128,
>
> -0.0181149908112366, -0.0179372197309418, -0.0179172441100772,
>
> -0.0178571428571429, -0.0174672489082969, -0.0174216027874564,
>
> -0.0171428571428572, -0.017017253604349, -0.0169252468265163,
>
> -0.0165094339622642, -0.0158730158730158, -0.0158415841584159,
>
> -0.0157247037374659, -0.0157089706490286, -0.0156250000000001,
>
> -0.0153846153846153, -0.0151668351870576, -0.0151589242053789,
>
> -0.0150489089541008, -0.0150262202501008, -0.0150081124932396,
>
> -0.0148196281468128, -0.0144251166737377, -0.0142857142857142,
>
> -0.0140638734251392, -0.0136986301369863, -0.0133333333333333,
>
> -0.0129464285714286, -0.0129449838187702, -0.0127813811522321,
>
> -0.0126030053320408, -0.0125721665147373, -0.0125, -0.0122160435399906,
>
> -0.0122116689280869, -0.0121019108280255, -0.0118747750989563,
>
> -0.0118277953189996, -0.0117107942973524, -0.0115172759138707,
>
> -0.0114087997381585, -0.0113924050632912, -0.0111524163568772,
>
> -0.0111248454882571, -0.0111111111111111, -0.0102570933795125,
>
> -0.0102040816326532, -0.00963463463463469, -0.00958657878969439,
>
> -0.00941028858218319, -0.00874453466583389, -0.00779588944011335,
>
> -0.00713620850139625, -0.00710720027075056, -0.00709219858156026,
>
> -0.00624999999999998, -0.00551977920883173, -0.00521499557217353,
>
> -0.00453998797354176, -0.00444444444444444, -0.00166389351081533,
>
> -0.00118483412322285, -0.00100704934541787, -0.000937500000000036,
>
> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
>
> 0.000218031178458569, 0.000796495420151402, 0.00167130919220062,
>
> 0.00190476190476193, 0.00350058343057173, 0.00363914958820145,
>
> 0.00432900432900424, 0.00456037942356804, 0.00477446915441642,
>
> 0.0050825509873745, 0.00525691029336935, 0.00603318250377083,
>
> 0.00652173913043472, 0.00733192494097176, 0.00747663551401869,
>
> 0.00760456273764256, 0.00812529439472442, 0.00991231414410967,
>
> 0.0101685066821615, 0.0106182565507793, 0.0109070034443169,
> 0.0115183246073298,
>
> 0.0115442244823827, 0.0127659574468085, 0.0128076846107665,
> 0.0135135135135135,
>
> 0.0140845070422535, 0.0150730098916627, 0.0159362549800796,
> 0.0172413793103449,
>
> 0.0176899063475547, 0.0186954715413378, 0.0187765706188003,
> 0.0195757403189066,
>
> 0.019607843137255, 0.0199999999999999, 0.0210526315789473,
> 0.0221979621542939,
>
> 0.0239410681399632, 0.0239999999999999, 0.025149051490515,
> 0.0260869565217392,
>
> 0.0262475696694749, 0.028180542563143, 0.0285714285714286,
> 0.0303030303030302,
>
> 0.0315904139433552, 0.0341864716636198, 0.0375782881002089,
> 0.038479809976247,
>
> 0.0387596899224806, 0.0416666666666667, 0.0428100987925357,
> 0.0428134556574923,
>
> 0.0437201907790144, 0.0451127819548872, 0.0460251046025105,
> 0.0487779511180447,
>
> 0.048975188781014, 0.0529872938632063, 0.0562390158172233,
> 0.0589335827876521,
>
> 0.0617551462621885, 0.0628115653040877, 0.0671812464265294,
> 0.0721784776902887,
>
> 0.0736842105263157, 0.0833333333333334, 0.083862394802894,
> 0.0970464135021097,
>
> 0.0971168437025795, 0.102272727272727, 0.111111111111111,
> 0.117117117117117,
>
> 0.123532699832309, 0.141304347826087, 0.179487179487179, 0.191268191268191,
>
> 0.205128205128205, 0.219020172910663, 0.271590909090909, 0.333333333333333
>
> )
>
>
> Now I want to estimate empirical PDF for interval of (-1, 1) including
> all points of Dat
>
> I have looked into the density() function, however it appears that,
> empirical density is estimated for equally distant points, which not
> necessarily contains actual supplied points (in my case, Dat)
>
> Is there any option to achieve the same?
>
> Thanks for your pointer.
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/
> posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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Re: Empirical density estimation

Jim Lemon-4
In reply to this post by Bogaso
Hi Christofer,
You may be looking for ecdf (stats) for a start, then working out a
way to translate the cumulative density values into probability
values.

Jim


On Mon, Mar 12, 2018 at 5:45 AM, Christofer Bogaso
<[hidden email]> wrote:

> Hi,
>
> Let say I have below vector of data-points :
>
> Dat = c(-0.444444444444444, -0.25, -0.237449799196787, -0.227467046669042,
>
> -0.227454464682363, -0.22, -0.214876033057851, -0.211781206171108,
>
> -0.199891067538126, -0.192920353982301, -0.192307692307692, -0.186046511627907,
>
> -0.184418145956608, -0.181818181818182, -0.181818181818182, -0.181266261925412,
>
> -0.181003118503119, -0.179064587973274, -0.178217821782178, -0.17809021675454,
>
> -0.177685950413223, -0.177570093457944, -0.176470588235294, -0.176470588235294,
>
> -0.174825741611282, -0.168021680216802, -0.166666666666667, -0.166666666666667,
>
> -0.166380789022298, -0.164209115281501, -0.164011246485473, -0.162689804772234,
>
> -0.162361623616236, -0.160161507402423, -0.16, -0.155038759689922,
>
> -0.154172560113154, -0.15311004784689, -0.151515151515152, -0.151462994836489,
>
> -0.151098901098901, -0.150537634408602, -0.150442477876106, -0.150406504065041,
>
> -0.149904214559387, -0.149882903981265, -0.149797570850202, -0.148496240601504,
>
> -0.148325358851675, -0.147540983606557, -0.147239263803681, -0.146989966555184,
>
> -0.14622641509434, -0.146095717884131, -0.145994832041344, -0.14572864321608,
>
> -0.145161290322581, -0.144292237442922, -0.144144144144144, -0.144021739130435,
>
> -0.14375, -0.142212189616253, -0.141122913505311, -0.140324963072378,
>
> -0.139344262295082, -0.13884007029877, -0.138356164383562, -0.137626262626263,
>
> -0.137142857142857, -0.136690647482014, -0.136577708006279, -0.136363636363636,
>
> -0.136094674556213, -0.135879774577332, -0.135586319218241, -0.135135135135135,
>
> -0.132780082987552, -0.132209405501331, -0.132023755139333, -0.131233595800525,
>
> -0.130434782608696, -0.130434782608696, -0.130268199233717, -0.128813559322034,
>
> -0.1284046692607, -0.128205128205128, -0.128182616330114, -0.127937336814621,
>
> -0.126283367556468, -0.125853658536585, -0.125448028673835, -0.125425564840607,
>
> -0.125311203319502, -0.125, -0.124401913875598, -0.124248496993988,
>
> -0.124031007751938, -0.123572170301142, -0.123188405797102, -0.122905027932961,
>
> -0.121666666666667, -0.121573685907772, -0.120658135283364, -0.120540019286403,
>
> -0.119858156028369, -0.11965811965812, -0.11965811965812, -0.119565217391304,
>
> -0.118942731277533, -0.117820324005891, -0.116257947320618, -0.115789473684211,
>
> -0.115683584819387, -0.115384615384615, -0.115281501340483, -0.114492753623188,
>
> -0.114357262103506, -0.114285714285714, -0.114035087719298, -0.113181972212809,
>
> -0.112790697674419, -0.112781954887218, -0.112195121951219, -0.112191473448018,
>
> -0.111111111111111, -0.111111111111111, -0.110813226094727, -0.110384300899428,
>
> -0.110147441457069, -0.110137672090113, -0.109913793103448, -0.109792284866469,
>
> -0.109375, -0.10919540229885, -0.109112709832134, -0.10844250363901,
>
> -0.107776617954071, -0.10752688172043, -0.107317073170732, -0.106674272675414,
>
> -0.106382978723404, -0.106100795755968, -0.106060606060606, -0.10595160235448,
>
> -0.105742474070326, -0.105263157894737, -0.104454685099846, -0.104283054003724,
>
> -0.103916449086162, -0.103723404255319, -0.103448275862069, -0.102737680438029,
>
> -0.10267471958585, -0.101696871753434, -0.100893997445721, -0.10041265474553,
>
> -0.100042983021706, -0.1, -0.0995111731843576, -0.099502487562189,
>
> -0.0994117647058824, -0.0991561181434598, -0.0989492119089317,
>
> -0.0988372093023255, -0.0983908045977012, -0.0983050847457627,
>
> -0.0977198697068404, -0.0974702380952382, -0.0973819695475956,
>
> -0.097345132743363, -0.0971472629144179, -0.0971438645980254,
>
> -0.0961538461538461, -0.096062667491239, -0.0957347238935687,
>
> -0.0956521739130435, -0.0954773869346733, -0.0954115076474873,
>
> -0.0952380952380952, -0.0951115834218915, -0.0950642007303569,
>
> -0.0949423247559894, -0.0947368421052631, -0.0946291560102303,
>
> -0.0945220193340494, -0.0944309927360775, -0.0943016759776536,
>
> -0.0942720763723149, -0.0941770647653002, -0.0940298507462686,
>
> -0.094017094017094, -0.0935672514619884, -0.0934579439252337,
>
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> 0.0101685066821615, 0.0106182565507793, 0.0109070034443169, 0.0115183246073298,
>
> 0.0115442244823827, 0.0127659574468085, 0.0128076846107665, 0.0135135135135135,
>
> 0.0140845070422535, 0.0150730098916627, 0.0159362549800796, 0.0172413793103449,
>
> 0.0176899063475547, 0.0186954715413378, 0.0187765706188003, 0.0195757403189066,
>
> 0.019607843137255, 0.0199999999999999, 0.0210526315789473, 0.0221979621542939,
>
> 0.0239410681399632, 0.0239999999999999, 0.025149051490515, 0.0260869565217392,
>
> 0.0262475696694749, 0.028180542563143, 0.0285714285714286, 0.0303030303030302,
>
> 0.0315904139433552, 0.0341864716636198, 0.0375782881002089, 0.038479809976247,
>
> 0.0387596899224806, 0.0416666666666667, 0.0428100987925357, 0.0428134556574923,
>
> 0.0437201907790144, 0.0451127819548872, 0.0460251046025105, 0.0487779511180447,
>
> 0.048975188781014, 0.0529872938632063, 0.0562390158172233, 0.0589335827876521,
>
> 0.0617551462621885, 0.0628115653040877, 0.0671812464265294, 0.0721784776902887,
>
> 0.0736842105263157, 0.0833333333333334, 0.083862394802894, 0.0970464135021097,
>
> 0.0971168437025795, 0.102272727272727, 0.111111111111111, 0.117117117117117,
>
> 0.123532699832309, 0.141304347826087, 0.179487179487179, 0.191268191268191,
>
> 0.205128205128205, 0.219020172910663, 0.271590909090909, 0.333333333333333
>
> )
>
>
> Now I want to estimate empirical PDF for interval of (-1, 1) including
> all points of Dat
>
> I have looked into the density() function, however it appears that,
> empirical density is estimated for equally distant points, which not
> necessarily contains actual supplied points (in my case, Dat)
>
> Is there any option to achieve the same?
>
> Thanks for your pointer.
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
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> and provide commented, minimal, self-contained, reproducible code.

______________________________________________
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Re: Empirical density estimation

Bogaso
In reply to this post by Bert Gunter-2
But for my reporting purpose, I need to generate a bell curve like
plot based on empirical PDF, that also contains original points.

Any idea would be helpful. Thanks,

On Mon, Mar 12, 2018 at 3:49 AM, Bert Gunter <[hidden email]> wrote:

> You need to re-read ?density and perhaps think again -- or do some study --
> about how a (kernel) density estimate works. The points at which the
> estimate is calculated are *not* the values given, nor should they be!
>
> Cheers,
> Bert
>
>
>
> Bert Gunter
>
> "The trouble with having an open mind is that people keep coming along and
> sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>
> On Sun, Mar 11, 2018 at 11:45 AM, Christofer Bogaso
> <[hidden email]> wrote:
>>
>> Hi,
>>
>> Let say I have below vector of data-points :
>>
>> Dat = c(-0.444444444444444, -0.25, -0.237449799196787, -0.227467046669042,
>>
>> -0.227454464682363, -0.22, -0.214876033057851, -0.211781206171108,
>>
>> -0.199891067538126, -0.192920353982301, -0.192307692307692,
>> -0.186046511627907,
>>
>> -0.184418145956608, -0.181818181818182, -0.181818181818182,
>> -0.181266261925412,
>>
>> -0.181003118503119, -0.179064587973274, -0.178217821782178,
>> -0.17809021675454,
>>
>> -0.177685950413223, -0.177570093457944, -0.176470588235294,
>> -0.176470588235294,
>>
>> -0.174825741611282, -0.168021680216802, -0.166666666666667,
>> -0.166666666666667,
>>
>> -0.166380789022298, -0.164209115281501, -0.164011246485473,
>> -0.162689804772234,
>>
>> -0.162361623616236, -0.160161507402423, -0.16, -0.155038759689922,
>>
>> -0.154172560113154, -0.15311004784689, -0.151515151515152,
>> -0.151462994836489,
>>
>> -0.151098901098901, -0.150537634408602, -0.150442477876106,
>> -0.150406504065041,
>>
>> -0.149904214559387, -0.149882903981265, -0.149797570850202,
>> -0.148496240601504,
>>
>> -0.148325358851675, -0.147540983606557, -0.147239263803681,
>> -0.146989966555184,
>>
>> -0.14622641509434, -0.146095717884131, -0.145994832041344,
>> -0.14572864321608,
>>
>> -0.145161290322581, -0.144292237442922, -0.144144144144144,
>> -0.144021739130435,
>>
>> -0.14375, -0.142212189616253, -0.141122913505311, -0.140324963072378,
>>
>> -0.139344262295082, -0.13884007029877, -0.138356164383562,
>> -0.137626262626263,
>>
>> -0.137142857142857, -0.136690647482014, -0.136577708006279,
>> -0.136363636363636,
>>
>> -0.136094674556213, -0.135879774577332, -0.135586319218241,
>> -0.135135135135135,
>>
>> -0.132780082987552, -0.132209405501331, -0.132023755139333,
>> -0.131233595800525,
>>
>> -0.130434782608696, -0.130434782608696, -0.130268199233717,
>> -0.128813559322034,
>>
>> -0.1284046692607, -0.128205128205128, -0.128182616330114,
>> -0.127937336814621,
>>
>> -0.126283367556468, -0.125853658536585, -0.125448028673835,
>> -0.125425564840607,
>>
>> -0.125311203319502, -0.125, -0.124401913875598, -0.124248496993988,
>>
>> -0.124031007751938, -0.123572170301142, -0.123188405797102,
>> -0.122905027932961,
>>
>> -0.121666666666667, -0.121573685907772, -0.120658135283364,
>> -0.120540019286403,
>>
>> -0.119858156028369, -0.11965811965812, -0.11965811965812,
>> -0.119565217391304,
>>
>> -0.118942731277533, -0.117820324005891, -0.116257947320618,
>> -0.115789473684211,
>>
>> -0.115683584819387, -0.115384615384615, -0.115281501340483,
>> -0.114492753623188,
>>
>> -0.114357262103506, -0.114285714285714, -0.114035087719298,
>> -0.113181972212809,
>>
>> -0.112790697674419, -0.112781954887218, -0.112195121951219,
>> -0.112191473448018,
>>
>> -0.111111111111111, -0.111111111111111, -0.110813226094727,
>> -0.110384300899428,
>>
>> -0.110147441457069, -0.110137672090113, -0.109913793103448,
>> -0.109792284866469,
>>
>> -0.109375, -0.10919540229885, -0.109112709832134, -0.10844250363901,
>>
>> -0.107776617954071, -0.10752688172043, -0.107317073170732,
>> -0.106674272675414,
>>
>> -0.106382978723404, -0.106100795755968, -0.106060606060606,
>> -0.10595160235448,
>>
>> -0.105742474070326, -0.105263157894737, -0.104454685099846,
>> -0.104283054003724,
>>
>> -0.103916449086162, -0.103723404255319, -0.103448275862069,
>> -0.102737680438029,
>>
>> -0.10267471958585, -0.101696871753434, -0.100893997445721,
>> -0.10041265474553,
>>
>> -0.100042983021706, -0.1, -0.0995111731843576, -0.099502487562189,
>>
>> -0.0994117647058824, -0.0991561181434598, -0.0989492119089317,
>>
>> -0.0988372093023255, -0.0983908045977012, -0.0983050847457627,
>>
>> -0.0977198697068404, -0.0974702380952382, -0.0973819695475956,
>>
>> -0.097345132743363, -0.0971472629144179, -0.0971438645980254,
>>
>> -0.0961538461538461, -0.096062667491239, -0.0957347238935687,
>>
>> -0.0956521739130435, -0.0954773869346733, -0.0954115076474873,
>>
>> -0.0952380952380952, -0.0951115834218915, -0.0950642007303569,
>>
>> -0.0949423247559894, -0.0947368421052631, -0.0946291560102303,
>>
>> -0.0945220193340494, -0.0944309927360775, -0.0943016759776536,
>>
>> -0.0942720763723149, -0.0941770647653002, -0.0940298507462686,
>>
>> -0.094017094017094, -0.0935672514619884, -0.0934579439252337,
>>
>> -0.0930232558139535, -0.0929772502472798, -0.0929054054054054,
>>
>> -0.0928778745255637, -0.0927700348432055, -0.0925266903914591,
>>
>> -0.0922502666192677, -0.0918094218415418, -0.0915254237288135,
>>
>> -0.0914774596906876, -0.0914662894860915, -0.0914285714285715,
>>
>> -0.0912322274881517, -0.090909090909091, -0.0909090909090909,
>>
>> -0.09079754601227, -0.0907071455016661, -0.0906593406593406,
>>
>> -0.0903614457831325, -0.0903323548906352, -0.09, -0.0897243107769424,
>>
>> -0.0896358543417368, -0.0895522388059702, -0.0895052902487847,
>>
>> -0.0891719745222929, -0.0888888888888888, -0.0887227819304518,
>>
>> -0.0887096774193548, -0.0886956521739131, -0.0884703196347032,
>>
>> -0.0884450784593437, -0.0884413309982488, -0.0883577310155536,
>>
>> -0.0883054892601431, -0.0882917466410749, -0.0881628999776236,
>>
>> -0.0881193929739248, -0.0880681818181819, -0.0878186968838525,
>>
>> -0.087719298245614, -0.0876010781671159, -0.0873634945397815,
>>
>> -0.0872641509433961, -0.0871512228728901, -0.0871032050299035,
>>
>> -0.0868133772309825, -0.0865384615384615, -0.0858895705521473,
>>
>> -0.085742525327403, -0.0855766209280403, -0.0854700854700855,
>>
>> -0.0853994490358125, -0.0853658536585365, -0.0851063829787235,
>>
>> -0.085048426150121, -0.0849673202614379, -0.084862385321101,
>>
>> -0.0843335637529065, -0.0843222985633979, -0.084315503173164,
>>
>> -0.0842105263157896, -0.0841423948220064, -0.0838323353293414,
>>
>> -0.0836501901140684, -0.083422459893048, -0.0833333333333334,
>>
>> -0.0833333333333333, -0.0827236916150815, -0.0826723611958512,
>>
>> -0.0826039387308535, -0.0824242424242424, -0.0821513002364065,
>>
>> -0.0820932539682539, -0.0820713238886174, -0.0818181818181818,
>>
>> -0.0816618911174786, -0.0816613868356214, -0.0816326530612244,
>>
>> -0.081619937694704, -0.0813748531139835, -0.0811965811965812,
>>
>> -0.0810372771474878, -0.0809095716552088, -0.0808823529411764,
>>
>> -0.0808414831492295, -0.0807511737089201, -0.0805722891566266,
>>
>> -0.0803474484256242, -0.0800000000000001, -0.0800000000000001,
>>
>> -0.0799584631360333, -0.0795941847087125, -0.0795930580490723,
>>
>> -0.0794701986754966, -0.0793650793650794, -0.0791855203619909,
>>
>> -0.0790273556231002, -0.0790273556231002, -0.0789473684210527,
>>
>> -0.0789473684210526, -0.0787545787545788, -0.0787461773700307,
>>
>> -0.0786724031960664, -0.0782122905027933, -0.078177727784027,
>>
>> -0.078125, -0.0778443113772455, -0.0776310524209684, -0.0775862068965517,
>>
>> -0.0775577557755776, -0.0773930753564156, -0.0772686433063791,
>>
>> -0.0771513353115727, -0.0771200000000001, -0.0770370370370371,
>>
>> -0.076923076923077, -0.076923076923077, -0.0769039940461424,
>>
>> -0.076592082616179, -0.0763425253991292, -0.0762886597938145,
>>
>> -0.0762886597938145, -0.0761565836298932, -0.0760869565217391,
>>
>> -0.07597645799893, -0.0758377425044092, -0.0757314974182444,
>>
>> -0.0755148741418765, -0.0754814305364511, -0.0754189944134078,
>>
>> -0.0752351097178683, -0.0750988142292491, -0.074935400516796,
>>
>> -0.0748663101604277, -0.0748031496062992, -0.0747663551401868,
>>
>> -0.0747295968534907, -0.0747028862478777, -0.0745967741935485,
>>
>> -0.0741784037558686, -0.0740740740740741, -0.0740740740740741,
>>
>> -0.0740740740740741, -0.073828125, -0.0736698499317872,
>> -0.0735877862595421,
>>
>> -0.0735824009102977, -0.0735632183908046, -0.0733944954128441,
>>
>> -0.0728862973760932, -0.0728279386712096, -0.0726480203414457,
>>
>> -0.0726329442282749, -0.072632190586868, -0.0725766664070006,
>>
>> -0.0724137931034483, -0.0722664432341852, -0.0719257540603249,
>>
>> -0.0717538461538461, -0.0716612377850163, -0.0715181932245923,
>>
>> -0.0714285714285715, -0.0714285714285713, -0.0710646285867525,
>>
>> -0.0708446866485014, -0.0708117443868739, -0.0708028321132845,
>>
>> -0.0706436420722135, -0.0705325930495579, -0.0705128205128205,
>>
>> -0.0705009276437847, -0.0704043019318861, -0.0702106318956871,
>>
>> -0.0701663201663202, -0.0700661736084078, -0.0699999999999999,
>>
>> -0.0695540857691487, -0.0692979983084297, -0.0691823899371069,
>>
>> -0.0691244239631336, -0.0690335305719921, -0.0689655172413792,
>>
>> -0.0688536409516944, -0.068450039339103, -0.0682332955832389,
>>
>> -0.0682261208576998, -0.0681818181818182, -0.0679035250463822,
>>
>> -0.0679012345679012, -0.0677966101694916, -0.0676384839650145,
>>
>> -0.0675675675675676, -0.0675241157556271, -0.067463706233988,
>>
>> -0.0674584323040379, -0.0668523676880222, -0.0666666666666667,
>>
>> -0.066526455612132, -0.0664206642066421, -0.066321243523316,
>>
>> -0.0662949194547709, -0.0662579580287669, -0.0662251655629139,
>>
>> -0.0661764705882353, -0.0661478599221789, -0.0657894736842105,
>>
>> -0.0657534246575342, -0.0654481924472518, -0.0652900974262034,
>>
>> -0.0652225100070638, -0.0651126106388572, -0.0650887573964497,
>>
>> -0.0650684931506849, -0.0650195058517555, -0.0649954627949184,
>>
>> -0.0649081209247184, -0.064891846921797, -0.0648899188876013,
>>
>> -0.0648148148148149, -0.0645962732919255, -0.0644599303135888,
>>
>> -0.0644171779141105, -0.0643564356435644, -0.064327485380117,
>>
>> -0.0642667310944672, -0.0641975308641976, -0.0641025641025641,
>>
>> -0.0639197041732701, -0.0638436482084691, -0.0635245901639343,
>>
>> -0.0634996041171813, -0.0632017594629008, -0.0631313131313131,
>>
>> -0.0630434782608695, -0.0629405840886203, -0.0629155024568842,
>>
>> -0.0628765060240964, -0.0628571428571429, -0.0625394819962098,
>>
>> -0.062476757158795, -0.06203552416592, -0.0620347394540943,
>> -0.0619971604354,
>>
>> -0.0619946091644204, -0.0619469026548672, -0.0619235836627141,
>>
>> -0.0618131868131868, -0.0617667356797793, -0.0617312601531677,
>>
>> -0.0616740088105726, -0.0614161849710983, -0.0613026819923372,
>>
>> -0.0612244897959185, -0.0610859728506788, -0.0610526315789473,
>>
>> -0.0610399397136398, -0.0610169491525424, -0.0609659540775929,
>>
>> -0.0608695652173912, -0.0606060606060606, -0.0606060606060606,
>>
>> -0.0604929051530994, -0.0604204204204204, -0.0603636363636364,
>>
>> -0.0602698650674663, -0.0602115541090318, -0.0599352051835853,
>>
>> -0.0599001663893511, -0.0596379126730565, -0.0594227504244482,
>>
>> -0.0587275693311581, -0.0587002096436059, -0.0586319218241041,
>>
>> -0.0586046511627907, -0.0584174190122145, -0.0584011488750599,
>>
>> -0.0583707504810776, -0.0579299691040165, -0.0579268292682926,
>>
>> -0.0579050097592712, -0.057608079558922, -0.0574712643678161,
>>
>> -0.0572450805008944, -0.0570958904109589, -0.0568263045032167,
>>
>> -0.0568181818181818, -0.0568181818181818, -0.0568031704095112,
>>
>> -0.0566301923974486, -0.0566037735849057, -0.0566037735849057,
>>
>> -0.0566037735849056, -0.0564433866031963, -0.0562770562770562,
>>
>> -0.0561576354679803, -0.0560928433268858, -0.0559006211180124,
>>
>> -0.0558213716108453, -0.055689240288759, -0.0554101893181468,
>>
>> -0.0553961597881263, -0.0553633217993079, -0.0553571428571429,
>>
>> -0.0553481577665964, -0.0553158101216163, -0.0553108174253549,
>>
>> -0.0548340548340548, -0.0546601261387525, -0.054590570719603,
>>
>> -0.0545001187366422, -0.0544511668107173, -0.0544274300932089,
>>
>> -0.0542372881355932, -0.0542168674698794, -0.0540540540540541,
>>
>> -0.053763440860215, -0.0537513997760358, -0.0536343468615424,
>>
>> -0.0535714285714286, -0.0534725518114223, -0.0529294274300931,
>>
>> -0.0528846153846155, -0.0528756957328386, -0.0526458340386634,
>>
>> -0.0526315789473684, -0.0525606469002696, -0.0525451559934318,
>>
>> -0.0525227460711332, -0.051948051948052, -0.051792828685259,
>>
>> -0.0517241379310345, -0.0513784461152881, -0.0513559322033898,
>>
>> -0.0512610211195407, -0.0512437810945274, -0.051150895140665,
>>
>> -0.0510695486616643, -0.0507726269315673, -0.0507377685736475,
>>
>> -0.0506575742815391, -0.0506024096385543, -0.0505494505494506,
>>
>> -0.0503194888178913, -0.0501567398119122, -0.05, -0.0499001996007984,
>>
>> -0.0498214285714285, -0.0497737556561087, -0.0497470489038785,
>>
>> -0.0494845360824741, -0.0493827160493827, -0.0492157923201731,
>>
>> -0.0491192897035657, -0.0489642184557439, -0.0488200324265898,
>>
>> -0.0488031366075114, -0.0485151426051161, -0.0483319076133448,
>>
>> -0.0481220657276996, -0.0480897675661234, -0.0480599647266314,
>>
>> -0.0480038022813688, -0.0479900280461202, -0.0479548660084627,
>>
>> -0.0478449164776243, -0.0475638051044084, -0.0475342709631477,
>>
>> -0.0473213579172271, -0.0472997462848857, -0.0472050636772667,
>>
>> -0.046890780551147, -0.0467625899280576, -0.046753107010276,
>>
>> -0.0466592011944754, -0.0465772759350741, -0.0465753424657535,
>>
>> -0.0464333781965007, -0.0463888365076373, -0.0463215258855587,
>>
>> -0.046281851274051, -0.0459946060208471, -0.0458715596330275,
>>
>> -0.0458563535911603, -0.0457367549668873, -0.0456500165398611,
>>
>> -0.0454373701114679, -0.0454265548766046, -0.0454183266932271,
>>
>> -0.045213508233324, -0.045182571340902, -0.0451018428709989,
>>
>> -0.0451018428709989, -0.044955044955045, -0.0444136016655101,
>>
>> -0.0443722943722945, -0.0442996742671011, -0.0442477876106195,
>>
>> -0.0442477876106195, -0.0441176470588236, -0.043982895540623,
>>
>> -0.0438184663536776, -0.0436363636363636, -0.043261231281198,
>>
>> -0.0432218514782339, -0.0431654676258993, -0.0424336600525938,
>>
>> -0.0423429781227946, -0.0423387096774193, -0.0420711974110032,
>>
>> -0.0420083118050095, -0.0420032310177707, -0.0417256011315418,
>>
>> -0.0416842105263158, -0.0416141235813367, -0.0414593698175788,
>>
>> -0.0413793103448276, -0.041320942582144, -0.0407865986890023,
>>
>> -0.0406158747013539, -0.0405803571428572, -0.0405643738977073,
>>
>> -0.040422053796998, -0.040268456375839, -0.0400500625782228,
>>
>> -0.0400449101796407, -0.04, -0.0399718147460123, -0.0399137001078749,
>>
>> -0.0399044464954666, -0.0398863290368415, -0.0398230088495575,
>>
>> -0.0394736842105263, -0.0393401015228426, -0.0392720306513411,
>>
>> -0.0392156862745098, -0.0388349514563106, -0.0386904761904763,
>>
>> -0.0384615384615385, -0.0382457345700217, -0.0382293762575454,
>>
>> -0.0381840048105834, -0.0380030474141795, -0.0379746835443038,
>>
>> -0.0379247280777747, -0.0376432078559739, -0.0375494071146245,
>>
>> -0.0375490837696336, -0.0373345788572318, -0.0372940156114484,
>>
>> -0.0371871275327772, -0.037037037037037, -0.0368133174791915,
>>
>> -0.0368098159509203, -0.0367231638418078, -0.0361445783132531,
>>
>> -0.0360915492957746, -0.0357142857142857, -0.0356663184599313,
>>
>> -0.0356413696552528, -0.035513103110458, -0.0353194103194103,
>>
>> -0.0352112676056338, -0.0350119904076739, -0.0349794238683129,
>>
>> -0.0349373764007909, -0.0349091600875106, -0.0347826086956522,
>>
>> -0.0347728547392037, -0.0347682119205298, -0.0346083788706739,
>>
>> -0.0344706296166022, -0.0344421548425081, -0.0341176470588236,
>>
>> -0.0338983050847458, -0.033457249070632, -0.0334208223972004,
>>
>> -0.0333333333333334, -0.0333333333333333, -0.0329670329670331,
>>
>> -0.0329144225014961, -0.0326797385620915, -0.0323033707865168,
>>
>> -0.0322118826055834, -0.0321750321750322, -0.0320890635232481,
>>
>> -0.0318302387267905, -0.0316666666666666, -0.0315586914688903,
>>
>> -0.0312606184165817, -0.030881017257039, -0.0308764940239045,
>>
>> -0.0305419952434597, -0.030406198638178, -0.0299651567944252,
>>
>> -0.029945999018164, -0.0298786181139121, -0.0295741147960329,
>>
>> -0.0293917033546227, -0.029171528588098, -0.0291327913279132,
>>
>> -0.0290497291974397, -0.0288721376760064, -0.0287704170466792,
>>
>> -0.0286236297198539, -0.0285714285714286, -0.0277575837684224,
>>
>> -0.0277085471338513, -0.0275897304892068, -0.0275526742301458,
>>
>> -0.027027027027027, -0.0270270270270269, -0.0269087523277468,
>>
>> -0.0268918695148203, -0.02676704307821, -0.026454253142356,
>> -0.0263157894736842,
>>
>> -0.0263157894736842, -0.0261660978384529, -0.025974025974026,
>>
>> -0.0257503107796129, -0.0255319148936171, -0.0254237288135594,
>>
>> -0.025297619047619, -0.0249174422095467, -0.0248888888888889,
>>
>> -0.024767619719967, -0.0246053853296194, -0.0245269796776454,
>>
>> -0.024390243902439, -0.0241935483870968, -0.0238907849829351,
>>
>> -0.0238153295944078, -0.0234413496961306, -0.0232558139534884,
>>
>> -0.0232558139534883, -0.0230392156862745, -0.0230360307147077,
>>
>> -0.0228847365106026, -0.0225806451612903, -0.0224519940915805,
>>
>> -0.0214786344110332, -0.0212360867018161, -0.0205245153933865,
>>
>> -0.0204170602339606, -0.0200986321764215, -0.0200729927007299,
>>
>> -0.0199828473413379, -0.0194174757281553, -0.0193536931818183,
>>
>> -0.0192885771543086, -0.019222732971166, -0.0191414840759143,
>>
>> -0.0189573459715641, -0.0188902007083826, -0.0186903321231681,
>>
>> -0.0184456468273487, -0.0183066361556064, -0.0182166826462128,
>>
>> -0.0181149908112366, -0.0179372197309418, -0.0179172441100772,
>>
>> -0.0178571428571429, -0.0174672489082969, -0.0174216027874564,
>>
>> -0.0171428571428572, -0.017017253604349, -0.0169252468265163,
>>
>> -0.0165094339622642, -0.0158730158730158, -0.0158415841584159,
>>
>> -0.0157247037374659, -0.0157089706490286, -0.0156250000000001,
>>
>> -0.0153846153846153, -0.0151668351870576, -0.0151589242053789,
>>
>> -0.0150489089541008, -0.0150262202501008, -0.0150081124932396,
>>
>> -0.0148196281468128, -0.0144251166737377, -0.0142857142857142,
>>
>> -0.0140638734251392, -0.0136986301369863, -0.0133333333333333,
>>
>> -0.0129464285714286, -0.0129449838187702, -0.0127813811522321,
>>
>> -0.0126030053320408, -0.0125721665147373, -0.0125, -0.0122160435399906,
>>
>> -0.0122116689280869, -0.0121019108280255, -0.0118747750989563,
>>
>> -0.0118277953189996, -0.0117107942973524, -0.0115172759138707,
>>
>> -0.0114087997381585, -0.0113924050632912, -0.0111524163568772,
>>
>> -0.0111248454882571, -0.0111111111111111, -0.0102570933795125,
>>
>> -0.0102040816326532, -0.00963463463463469, -0.00958657878969439,
>>
>> -0.00941028858218319, -0.00874453466583389, -0.00779588944011335,
>>
>> -0.00713620850139625, -0.00710720027075056, -0.00709219858156026,
>>
>> -0.00624999999999998, -0.00551977920883173, -0.00521499557217353,
>>
>> -0.00453998797354176, -0.00444444444444444, -0.00166389351081533,
>>
>> -0.00118483412322285, -0.00100704934541787, -0.000937500000000036,
>>
>> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
>>
>> 0.000218031178458569, 0.000796495420151402, 0.00167130919220062,
>>
>> 0.00190476190476193, 0.00350058343057173, 0.00363914958820145,
>>
>> 0.00432900432900424, 0.00456037942356804, 0.00477446915441642,
>>
>> 0.0050825509873745, 0.00525691029336935, 0.00603318250377083,
>>
>> 0.00652173913043472, 0.00733192494097176, 0.00747663551401869,
>>
>> 0.00760456273764256, 0.00812529439472442, 0.00991231414410967,
>>
>> 0.0101685066821615, 0.0106182565507793, 0.0109070034443169,
>> 0.0115183246073298,
>>
>> 0.0115442244823827, 0.0127659574468085, 0.0128076846107665,
>> 0.0135135135135135,
>>
>> 0.0140845070422535, 0.0150730098916627, 0.0159362549800796,
>> 0.0172413793103449,
>>
>> 0.0176899063475547, 0.0186954715413378, 0.0187765706188003,
>> 0.0195757403189066,
>>
>> 0.019607843137255, 0.0199999999999999, 0.0210526315789473,
>> 0.0221979621542939,
>>
>> 0.0239410681399632, 0.0239999999999999, 0.025149051490515,
>> 0.0260869565217392,
>>
>> 0.0262475696694749, 0.028180542563143, 0.0285714285714286,
>> 0.0303030303030302,
>>
>> 0.0315904139433552, 0.0341864716636198, 0.0375782881002089,
>> 0.038479809976247,
>>
>> 0.0387596899224806, 0.0416666666666667, 0.0428100987925357,
>> 0.0428134556574923,
>>
>> 0.0437201907790144, 0.0451127819548872, 0.0460251046025105,
>> 0.0487779511180447,
>>
>> 0.048975188781014, 0.0529872938632063, 0.0562390158172233,
>> 0.0589335827876521,
>>
>> 0.0617551462621885, 0.0628115653040877, 0.0671812464265294,
>> 0.0721784776902887,
>>
>> 0.0736842105263157, 0.0833333333333334, 0.083862394802894,
>> 0.0970464135021097,
>>
>> 0.0971168437025795, 0.102272727272727, 0.111111111111111,
>> 0.117117117117117,
>>
>> 0.123532699832309, 0.141304347826087, 0.179487179487179,
>> 0.191268191268191,
>>
>> 0.205128205128205, 0.219020172910663, 0.271590909090909, 0.333333333333333
>>
>> )
>>
>>
>> Now I want to estimate empirical PDF for interval of (-1, 1) including
>> all points of Dat
>>
>> I have looked into the density() function, however it appears that,
>> empirical density is estimated for equally distant points, which not
>> necessarily contains actual supplied points (in my case, Dat)
>>
>> Is there any option to achieve the same?
>>
>> Thanks for your pointer.
>>
>> ______________________________________________
>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>
>

______________________________________________
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Empirical density estimation

Daniel Nordlund-3
On 3/11/2018 3:35 PM, Christofer Bogaso wrote:
> But for my reporting purpose, I need to generate a bell curve like
> plot based on empirical PDF, that also contains original points.
>
> Any idea would be helpful. Thanks,
>


Christofer,

something like the following may get you what you want:

## get the kernel density estimate
dens <- density(Dat)

## estimate the density at your original points
dnew <- approx(dens$x,dens$y,xout=Dat)

## plot kernel density estimate
plot(dx)

## add your original values with the estimated density
points(dnew, pch=1, cex=0.5, col="red")


Hope this is helpful,

Dan

--
Daniel Nordlund
Port Townsend, WA  USA

> On Mon, Mar 12, 2018 at 3:49 AM, Bert Gunter <[hidden email]> wrote:
>> You need to re-read ?density and perhaps think again -- or do some study --
>> about how a (kernel) density estimate works. The points at which the
>> estimate is calculated are *not* the values given, nor should they be!
>>
>> Cheers,
>> Bert
>>
>>
>>
>> Bert Gunter
>>
>> "The trouble with having an open mind is that people keep coming along and
>> sticking things into it."
>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>
>> On Sun, Mar 11, 2018 at 11:45 AM, Christofer Bogaso
>> <[hidden email]> wrote:
>>>
>>> Hi,
>>>
>>> Let say I have below vector of data-points :
>>>
>>> Dat = c(-0.444444444444444, -0.25, -0.237449799196787, -0.227467046669042,
>>>
>>> -0.227454464682363, -0.22, -0.214876033057851, -0.211781206171108,
>>>
>>> -0.199891067538126, -0.192920353982301, -0.192307692307692,
>>> -0.186046511627907,
>>>
>>> -0.184418145956608, -0.181818181818182, -0.181818181818182,
>>> -0.181266261925412,
>>>
>>> -0.181003118503119, -0.179064587973274, -0.178217821782178,
>>> -0.17809021675454,
>>>
>>> -0.177685950413223, -0.177570093457944, -0.176470588235294,
>>> -0.176470588235294,
>>>
>>> -0.174825741611282, -0.168021680216802, -0.166666666666667,
>>> -0.166666666666667,
>>>
>>> -0.166380789022298, -0.164209115281501, -0.164011246485473,
>>> -0.162689804772234,
>>>
>>> -0.162361623616236, -0.160161507402423, -0.16, -0.155038759689922,
>>>
>>> -0.154172560113154, -0.15311004784689, -0.151515151515152,
>>> -0.151462994836489,
>>>
>>> -0.151098901098901, -0.150537634408602, -0.150442477876106,
>>> -0.150406504065041,
>>>
>>> -0.149904214559387, -0.149882903981265, -0.149797570850202,
>>> -0.148496240601504,
>>>
>>> -0.148325358851675, -0.147540983606557, -0.147239263803681,
>>> -0.146989966555184,
>>>
>>> -0.14622641509434, -0.146095717884131, -0.145994832041344,
>>> -0.14572864321608,
>>>
>>> -0.145161290322581, -0.144292237442922, -0.144144144144144,
>>> -0.144021739130435,
>>>
>>> -0.14375, -0.142212189616253, -0.141122913505311, -0.140324963072378,
>>>
>>> -0.139344262295082, -0.13884007029877, -0.138356164383562,
>>> -0.137626262626263,
>>>
>>> -0.137142857142857, -0.136690647482014, -0.136577708006279,
>>> -0.136363636363636,
>>>
>>> -0.136094674556213, -0.135879774577332, -0.135586319218241,
>>> -0.135135135135135,
>>>
>>> -0.132780082987552, -0.132209405501331, -0.132023755139333,
>>> -0.131233595800525,
>>>
>>> -0.130434782608696, -0.130434782608696, -0.130268199233717,
>>> -0.128813559322034,
>>>
>>> -0.1284046692607, -0.128205128205128, -0.128182616330114,
>>> -0.127937336814621,
>>>
>>> -0.126283367556468, -0.125853658536585, -0.125448028673835,
>>> -0.125425564840607,
>>>
>>> -0.125311203319502, -0.125, -0.124401913875598, -0.124248496993988,
>>>
>>> -0.124031007751938, -0.123572170301142, -0.123188405797102,
>>> -0.122905027932961,
>>>
>>> -0.121666666666667, -0.121573685907772, -0.120658135283364,
>>> -0.120540019286403,
>>>
>>> -0.119858156028369, -0.11965811965812, -0.11965811965812,
>>> -0.119565217391304,
>>>
>>> -0.118942731277533, -0.117820324005891, -0.116257947320618,
>>> -0.115789473684211,
>>>
>>> -0.115683584819387, -0.115384615384615, -0.115281501340483,
>>> -0.114492753623188,
>>>
>>> -0.114357262103506, -0.114285714285714, -0.114035087719298,
>>> -0.113181972212809,
>>>
>>> -0.112790697674419, -0.112781954887218, -0.112195121951219,
>>> -0.112191473448018,
>>>
>>> -0.111111111111111, -0.111111111111111, -0.110813226094727,
>>> -0.110384300899428,
>>>
>>> -0.110147441457069, -0.110137672090113, -0.109913793103448,
>>> -0.109792284866469,
>>>
>>> -0.109375, -0.10919540229885, -0.109112709832134, -0.10844250363901,
>>>
>>> -0.107776617954071, -0.10752688172043, -0.107317073170732,
>>> -0.106674272675414,
>>>
>>> -0.106382978723404, -0.106100795755968, -0.106060606060606,
>>> -0.10595160235448,
>>>
>>> -0.105742474070326, -0.105263157894737, -0.104454685099846,
>>> -0.104283054003724,
>>>
>>> -0.103916449086162, -0.103723404255319, -0.103448275862069,
>>> -0.102737680438029,
>>>
>>> -0.10267471958585, -0.101696871753434, -0.100893997445721,
>>> -0.10041265474553,
>>>
>>> -0.100042983021706, -0.1, -0.0995111731843576, -0.099502487562189,
>>>
>>> -0.0994117647058824, -0.0991561181434598, -0.0989492119089317,
>>>
>>> -0.0988372093023255, -0.0983908045977012, -0.0983050847457627,
>>>
>>> -0.0977198697068404, -0.0974702380952382, -0.0973819695475956,
>>>
>>> -0.097345132743363, -0.0971472629144179, -0.0971438645980254,
>>>
>>> -0.0961538461538461, -0.096062667491239, -0.0957347238935687,
>>>
>>> -0.0956521739130435, -0.0954773869346733, -0.0954115076474873,
>>>
>>> -0.0952380952380952, -0.0951115834218915, -0.0950642007303569,
>>>
>>> -0.0949423247559894, -0.0947368421052631, -0.0946291560102303,
>>>
>>> -0.0945220193340494, -0.0944309927360775, -0.0943016759776536,
>>>
>>> -0.0942720763723149, -0.0941770647653002, -0.0940298507462686,
>>>
>>> -0.094017094017094, -0.0935672514619884, -0.0934579439252337,
>>>
>>> -0.0930232558139535, -0.0929772502472798, -0.0929054054054054,
>>>
>>> -0.0928778745255637, -0.0927700348432055, -0.0925266903914591,
>>>
>>> -0.0922502666192677, -0.0918094218415418, -0.0915254237288135,
>>>
>>> -0.0914774596906876, -0.0914662894860915, -0.0914285714285715,
>>>
>>> -0.0912322274881517, -0.090909090909091, -0.0909090909090909,
>>>
>>> -0.09079754601227, -0.0907071455016661, -0.0906593406593406,
>>>
>>> -0.0903614457831325, -0.0903323548906352, -0.09, -0.0897243107769424,
>>>
>>> -0.0896358543417368, -0.0895522388059702, -0.0895052902487847,
>>>
>>> -0.0891719745222929, -0.0888888888888888, -0.0887227819304518,
>>>
>>> -0.0887096774193548, -0.0886956521739131, -0.0884703196347032,
>>>
>>> -0.0884450784593437, -0.0884413309982488, -0.0883577310155536,
>>>
>>> -0.0883054892601431, -0.0882917466410749, -0.0881628999776236,
>>>
>>> -0.0881193929739248, -0.0880681818181819, -0.0878186968838525,
>>>
>>> -0.087719298245614, -0.0876010781671159, -0.0873634945397815,
>>>
>>> -0.0872641509433961, -0.0871512228728901, -0.0871032050299035,
>>>
>>> -0.0868133772309825, -0.0865384615384615, -0.0858895705521473,
>>>
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>>> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
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>>>
>>> 0.0971168437025795, 0.102272727272727, 0.111111111111111,
>>> 0.117117117117117,
>>>
>>> 0.123532699832309, 0.141304347826087, 0.179487179487179,
>>> 0.191268191268191,
>>>
>>> 0.205128205128205, 0.219020172910663, 0.271590909090909, 0.333333333333333
>>>
>>> )
>>>
>>>
>>> Now I want to estimate empirical PDF for interval of (-1, 1) including
>>> all points of Dat
>>>
>>> I have looked into the density() function, however it appears that,
>>> empirical density is estimated for equally distant points, which not
>>> necessarily contains actual supplied points (in my case, Dat)
>>>
>>> Is there any option to achieve the same?
>>>
>>> Thanks for your pointer.
>>>
>>> ______________________________________________
>>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>
>>
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
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Re: Empirical density estimation

Jeff Newmiller
cwhmisc package provides essentially the algorithm outlined by Dan.

If you want answers outside your original data (extrapolation) then the
following code at least won't give broken answers, though it is not
necessarily any more "correct" for extrapolation than the approx solution
is.

Regarding "needing this for reporting", do thoroughly read ?density as
Bert suggested, because the bandwidth parameter affects your answers and
there are various historical recommendations for choosing possible
bandwidth values, and really no "right" answer.

############
smoothed.df2 <- function ( d ) {
     F <- cumsum( d$y )
     F <- F / F[ length( F ) ] * ( length( F ) - 0.5 ) / length( F )
     eF <- splinefun( d$x, qlogis( F ), "monoH.FC" )
     function( x ) {
         efx <- eF( x )
         plogis( efx )
     }
}

set.seed( 42 )
Dat <- c( rnorm( 100, 1 ), rnorm( 100, 5 ) )

d <- density( Dat )

CDF1 <- cwhmisc::smoothed.df( d )
plot( Dat, CDF1( Dat ) )

CDF2 <- smoothed.df2( d )
plot( Dat, CDF2( Dat ) )

CDF1( -5 ) # <0
CDF2( -5 ) # >0
############

On Sun, 11 Mar 2018, Daniel Nordlund wrote:

> On 3/11/2018 3:35 PM, Christofer Bogaso wrote:
>> But for my reporting purpose, I need to generate a bell curve like
>> plot based on empirical PDF, that also contains original points.
>>
>> Any idea would be helpful. Thanks,
>>
>
>
> Christofer,
>
> something like the following may get you what you want:
>
> ## get the kernel density estimate
> dens <- density(Dat)
>
> ## estimate the density at your original points
> dnew <- approx(dens$x,dens$y,xout=Dat)
>
> ## plot kernel density estimate
> plot(dx)
>
> ## add your original values with the estimated density
> points(dnew, pch=1, cex=0.5, col="red")
>
>
> Hope this is helpful,
>
> Dan
>
> --
> Daniel Nordlund
> Port Townsend, WA  USA
>
>> On Mon, Mar 12, 2018 at 3:49 AM, Bert Gunter <[hidden email]>
>> wrote:
>>> You need to re-read ?density and perhaps think again -- or do some study
>>> --
>>> about how a (kernel) density estimate works. The points at which the
>>> estimate is calculated are *not* the values given, nor should they be!
>>>
>>> Cheers,
>>> Bert
>>>
>>>
>>>
>>> Bert Gunter
>>>
>>> "The trouble with having an open mind is that people keep coming along and
>>> sticking things into it."
>>> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
>>>
>>> On Sun, Mar 11, 2018 at 11:45 AM, Christofer Bogaso
>>> <[hidden email]> wrote:
>>>>
>>>> Hi,
>>>>
>>>> Let say I have below vector of data-points :
>>>>
>>>> Dat = c(-0.444444444444444, -0.25, -0.237449799196787,
>>>> -0.227467046669042,
>>>>
>>>> -0.227454464682363, -0.22, -0.214876033057851, -0.211781206171108,
>>>>
>>>> -0.199891067538126, -0.192920353982301, -0.192307692307692,
>>>> -0.186046511627907,
>>>>
>>>> -0.184418145956608, -0.181818181818182, -0.181818181818182,
>>>> -0.181266261925412,
>>>>
>>>> -0.181003118503119, -0.179064587973274, -0.178217821782178,
>>>> -0.17809021675454,
>>>>
>>>> -0.177685950413223, -0.177570093457944, -0.176470588235294,
>>>> -0.176470588235294,
>>>>
>>>> -0.174825741611282, -0.168021680216802, -0.166666666666667,
>>>> -0.166666666666667,
>>>>
>>>> -0.166380789022298, -0.164209115281501, -0.164011246485473,
>>>> -0.162689804772234,
>>>>
>>>> -0.162361623616236, -0.160161507402423, -0.16, -0.155038759689922,
>>>>
>>>> -0.154172560113154, -0.15311004784689, -0.151515151515152,
>>>> -0.151462994836489,
>>>>
>>>> -0.151098901098901, -0.150537634408602, -0.150442477876106,
>>>> -0.150406504065041,
>>>>
>>>> -0.149904214559387, -0.149882903981265, -0.149797570850202,
>>>> -0.148496240601504,
>>>>
>>>> -0.148325358851675, -0.147540983606557, -0.147239263803681,
>>>> -0.146989966555184,
>>>>
>>>> -0.14622641509434, -0.146095717884131, -0.145994832041344,
>>>> -0.14572864321608,
>>>>
>>>> -0.145161290322581, -0.144292237442922, -0.144144144144144,
>>>> -0.144021739130435,
>>>>
>>>> -0.14375, -0.142212189616253, -0.141122913505311, -0.140324963072378,
>>>>
>>>> -0.139344262295082, -0.13884007029877, -0.138356164383562,
>>>> -0.137626262626263,
>>>>
>>>> -0.137142857142857, -0.136690647482014, -0.136577708006279,
>>>> -0.136363636363636,
>>>>
>>>> -0.136094674556213, -0.135879774577332, -0.135586319218241,
>>>> -0.135135135135135,
>>>>
>>>> -0.132780082987552, -0.132209405501331, -0.132023755139333,
>>>> -0.131233595800525,
>>>>
>>>> -0.130434782608696, -0.130434782608696, -0.130268199233717,
>>>> -0.128813559322034,
>>>>
>>>> -0.1284046692607, -0.128205128205128, -0.128182616330114,
>>>> -0.127937336814621,
>>>>
>>>> -0.126283367556468, -0.125853658536585, -0.125448028673835,
>>>> -0.125425564840607,
>>>>
>>>> -0.125311203319502, -0.125, -0.124401913875598, -0.124248496993988,
>>>>
>>>> -0.124031007751938, -0.123572170301142, -0.123188405797102,
>>>> -0.122905027932961,
>>>>
>>>> -0.121666666666667, -0.121573685907772, -0.120658135283364,
>>>> -0.120540019286403,
>>>>
>>>> -0.119858156028369, -0.11965811965812, -0.11965811965812,
>>>> -0.119565217391304,
>>>>
>>>> -0.118942731277533, -0.117820324005891, -0.116257947320618,
>>>> -0.115789473684211,
>>>>
>>>> -0.115683584819387, -0.115384615384615, -0.115281501340483,
>>>> -0.114492753623188,
>>>>
>>>> -0.114357262103506, -0.114285714285714, -0.114035087719298,
>>>> -0.113181972212809,
>>>>
>>>> -0.112790697674419, -0.112781954887218, -0.112195121951219,
>>>> -0.112191473448018,
>>>>
>>>> -0.111111111111111, -0.111111111111111, -0.110813226094727,
>>>> -0.110384300899428,
>>>>
>>>> -0.110147441457069, -0.110137672090113, -0.109913793103448,
>>>> -0.109792284866469,
>>>>
>>>> -0.109375, -0.10919540229885, -0.109112709832134, -0.10844250363901,
>>>>
>>>> -0.107776617954071, -0.10752688172043, -0.107317073170732,
>>>> -0.106674272675414,
>>>>
>>>> -0.106382978723404, -0.106100795755968, -0.106060606060606,
>>>> -0.10595160235448,
>>>>
>>>> -0.105742474070326, -0.105263157894737, -0.104454685099846,
>>>> -0.104283054003724,
>>>>
>>>> -0.103916449086162, -0.103723404255319, -0.103448275862069,
>>>> -0.102737680438029,
>>>>
>>>> -0.10267471958585, -0.101696871753434, -0.100893997445721,
>>>> -0.10041265474553,
>>>>
>>>> -0.100042983021706, -0.1, -0.0995111731843576, -0.099502487562189,
>>>>
>>>> -0.0994117647058824, -0.0991561181434598, -0.0989492119089317,
>>>>
>>>> -0.0988372093023255, -0.0983908045977012, -0.0983050847457627,
>>>>
>>>> -0.0977198697068404, -0.0974702380952382, -0.0973819695475956,
>>>>
>>>> -0.097345132743363, -0.0971472629144179, -0.0971438645980254,
>>>>
>>>> -0.0961538461538461, -0.096062667491239, -0.0957347238935687,
>>>>
>>>> -0.0956521739130435, -0.0954773869346733, -0.0954115076474873,
>>>>
>>>> -0.0952380952380952, -0.0951115834218915, -0.0950642007303569,
>>>>
>>>> -0.0949423247559894, -0.0947368421052631, -0.0946291560102303,
>>>>
>>>> -0.0945220193340494, -0.0944309927360775, -0.0943016759776536,
>>>>
>>>> -0.0942720763723149, -0.0941770647653002, -0.0940298507462686,
>>>>
>>>> -0.094017094017094, -0.0935672514619884, -0.0934579439252337,
>>>>
>>>> -0.0930232558139535, -0.0929772502472798, -0.0929054054054054,
>>>>
>>>> -0.0928778745255637, -0.0927700348432055, -0.0925266903914591,
>>>>
>>>> -0.0922502666192677, -0.0918094218415418, -0.0915254237288135,
>>>>
>>>> -0.0914774596906876, -0.0914662894860915, -0.0914285714285715,
>>>>
>>>> -0.0912322274881517, -0.090909090909091, -0.0909090909090909,
>>>>
>>>> -0.09079754601227, -0.0907071455016661, -0.0906593406593406,
>>>>
>>>> -0.0903614457831325, -0.0903323548906352, -0.09, -0.0897243107769424,
>>>>
>>>> -0.0896358543417368, -0.0895522388059702, -0.0895052902487847,
>>>>
>>>> -0.0891719745222929, -0.0888888888888888, -0.0887227819304518,
>>>>
>>>> -0.0887096774193548, -0.0886956521739131, -0.0884703196347032,
>>>>
>>>> -0.0884450784593437, -0.0884413309982488, -0.0883577310155536,
>>>>
>>>> -0.0883054892601431, -0.0882917466410749, -0.0881628999776236,
>>>>
>>>> -0.0881193929739248, -0.0880681818181819, -0.0878186968838525,
>>>>
>>>> -0.087719298245614, -0.0876010781671159, -0.0873634945397815,
>>>>
>>>> -0.0872641509433961, -0.0871512228728901, -0.0871032050299035,
>>>>
>>>> -0.0868133772309825, -0.0865384615384615, -0.0858895705521473,
>>>>
>>>> -0.085742525327403, -0.0855766209280403, -0.0854700854700855,
>>>>
>>>> -0.0853994490358125, -0.0853658536585365, -0.0851063829787235,
>>>>
>>>> -0.085048426150121, -0.0849673202614379, -0.084862385321101,
>>>>
>>>> -0.0843335637529065, -0.0843222985633979, -0.084315503173164,
>>>>
>>>> -0.0842105263157896, -0.0841423948220064, -0.0838323353293414,
>>>>
>>>> -0.0836501901140684, -0.083422459893048, -0.0833333333333334,
>>>>
>>>> -0.0833333333333333, -0.0827236916150815, -0.0826723611958512,
>>>>
>>>> -0.0826039387308535, -0.0824242424242424, -0.0821513002364065,
>>>>
>>>> -0.0820932539682539, -0.0820713238886174, -0.0818181818181818,
>>>>
>>>> -0.0816618911174786, -0.0816613868356214, -0.0816326530612244,
>>>>
>>>> -0.081619937694704, -0.0813748531139835, -0.0811965811965812,
>>>>
>>>> -0.0810372771474878, -0.0809095716552088, -0.0808823529411764,
>>>>
>>>> -0.0808414831492295, -0.0807511737089201, -0.0805722891566266,
>>>>
>>>> -0.0803474484256242, -0.0800000000000001, -0.0800000000000001,
>>>>
>>>> -0.0799584631360333, -0.0795941847087125, -0.0795930580490723,
>>>>
>>>> -0.0794701986754966, -0.0793650793650794, -0.0791855203619909,
>>>>
>>>> -0.0790273556231002, -0.0790273556231002, -0.0789473684210527,
>>>>
>>>> -0.0789473684210526, -0.0787545787545788, -0.0787461773700307,
>>>>
>>>> -0.0786724031960664, -0.0782122905027933, -0.078177727784027,
>>>>
>>>> -0.078125, -0.0778443113772455, -0.0776310524209684, -0.0775862068965517,
>>>>
>>>> -0.0775577557755776, -0.0773930753564156, -0.0772686433063791,
>>>>
>>>> -0.0771513353115727, -0.0771200000000001, -0.0770370370370371,
>>>>
>>>> -0.076923076923077, -0.076923076923077, -0.0769039940461424,
>>>>
>>>> -0.076592082616179, -0.0763425253991292, -0.0762886597938145,
>>>>
>>>> -0.0762886597938145, -0.0761565836298932, -0.0760869565217391,
>>>>
>>>> -0.07597645799893, -0.0758377425044092, -0.0757314974182444,
>>>>
>>>> -0.0755148741418765, -0.0754814305364511, -0.0754189944134078,
>>>>
>>>> -0.0752351097178683, -0.0750988142292491, -0.074935400516796,
>>>>
>>>> -0.0748663101604277, -0.0748031496062992, -0.0747663551401868,
>>>>
>>>> -0.0747295968534907, -0.0747028862478777, -0.0745967741935485,
>>>>
>>>> -0.0741784037558686, -0.0740740740740741, -0.0740740740740741,
>>>>
>>>> -0.0740740740740741, -0.073828125, -0.0736698499317872,
>>>> -0.0735877862595421,
>>>>
>>>> -0.0735824009102977, -0.0735632183908046, -0.0733944954128441,
>>>>
>>>> -0.0728862973760932, -0.0728279386712096, -0.0726480203414457,
>>>>
>>>> -0.0726329442282749, -0.072632190586868, -0.0725766664070006,
>>>>
>>>> -0.0724137931034483, -0.0722664432341852, -0.0719257540603249,
>>>>
>>>> -0.0717538461538461, -0.0716612377850163, -0.0715181932245923,
>>>>
>>>> -0.0714285714285715, -0.0714285714285713, -0.0710646285867525,
>>>>
>>>> -0.0708446866485014, -0.0708117443868739, -0.0708028321132845,
>>>>
>>>> -0.0706436420722135, -0.0705325930495579, -0.0705128205128205,
>>>>
>>>> -0.0705009276437847, -0.0704043019318861, -0.0702106318956871,
>>>>
>>>> -0.0701663201663202, -0.0700661736084078, -0.0699999999999999,
>>>>
>>>> -0.0695540857691487, -0.0692979983084297, -0.0691823899371069,
>>>>
>>>> -0.0691244239631336, -0.0690335305719921, -0.0689655172413792,
>>>>
>>>> -0.0688536409516944, -0.068450039339103, -0.0682332955832389,
>>>>
>>>> -0.0682261208576998, -0.0681818181818182, -0.0679035250463822,
>>>>
>>>> -0.0679012345679012, -0.0677966101694916, -0.0676384839650145,
>>>>
>>>> -0.0675675675675676, -0.0675241157556271, -0.067463706233988,
>>>>
>>>> -0.0674584323040379, -0.0668523676880222, -0.0666666666666667,
>>>>
>>>> -0.066526455612132, -0.0664206642066421, -0.066321243523316,
>>>>
>>>> -0.0662949194547709, -0.0662579580287669, -0.0662251655629139,
>>>>
>>>> -0.0661764705882353, -0.0661478599221789, -0.0657894736842105,
>>>>
>>>> -0.0657534246575342, -0.0654481924472518, -0.0652900974262034,
>>>>
>>>> -0.0652225100070638, -0.0651126106388572, -0.0650887573964497,
>>>>
>>>> -0.0650684931506849, -0.0650195058517555, -0.0649954627949184,
>>>>
>>>> -0.0649081209247184, -0.064891846921797, -0.0648899188876013,
>>>>
>>>> -0.0648148148148149, -0.0645962732919255, -0.0644599303135888,
>>>>
>>>> -0.0644171779141105, -0.0643564356435644, -0.064327485380117,
>>>>
>>>> -0.0642667310944672, -0.0641975308641976, -0.0641025641025641,
>>>>
>>>> -0.0639197041732701, -0.0638436482084691, -0.0635245901639343,
>>>>
>>>> -0.0634996041171813, -0.0632017594629008, -0.0631313131313131,
>>>>
>>>> -0.0630434782608695, -0.0629405840886203, -0.0629155024568842,
>>>>
>>>> -0.0628765060240964, -0.0628571428571429, -0.0625394819962098,
>>>>
>>>> -0.062476757158795, -0.06203552416592, -0.0620347394540943,
>>>> -0.0619971604354,
>>>>
>>>> -0.0619946091644204, -0.0619469026548672, -0.0619235836627141,
>>>>
>>>> -0.0618131868131868, -0.0617667356797793, -0.0617312601531677,
>>>>
>>>> -0.0616740088105726, -0.0614161849710983, -0.0613026819923372,
>>>>
>>>> -0.0612244897959185, -0.0610859728506788, -0.0610526315789473,
>>>>
>>>> -0.0610399397136398, -0.0610169491525424, -0.0609659540775929,
>>>>
>>>> -0.0608695652173912, -0.0606060606060606, -0.0606060606060606,
>>>>
>>>> -0.0604929051530994, -0.0604204204204204, -0.0603636363636364,
>>>>
>>>> -0.0602698650674663, -0.0602115541090318, -0.0599352051835853,
>>>>
>>>> -0.0599001663893511, -0.0596379126730565, -0.0594227504244482,
>>>>
>>>> -0.0587275693311581, -0.0587002096436059, -0.0586319218241041,
>>>>
>>>> -0.0586046511627907, -0.0584174190122145, -0.0584011488750599,
>>>>
>>>> -0.0583707504810776, -0.0579299691040165, -0.0579268292682926,
>>>>
>>>> -0.0579050097592712, -0.057608079558922, -0.0574712643678161,
>>>>
>>>> -0.0572450805008944, -0.0570958904109589, -0.0568263045032167,
>>>>
>>>> -0.0568181818181818, -0.0568181818181818, -0.0568031704095112,
>>>>
>>>> -0.0566301923974486, -0.0566037735849057, -0.0566037735849057,
>>>>
>>>> -0.0566037735849056, -0.0564433866031963, -0.0562770562770562,
>>>>
>>>> -0.0561576354679803, -0.0560928433268858, -0.0559006211180124,
>>>>
>>>> -0.0558213716108453, -0.055689240288759, -0.0554101893181468,
>>>>
>>>> -0.0553961597881263, -0.0553633217993079, -0.0553571428571429,
>>>>
>>>> -0.0553481577665964, -0.0553158101216163, -0.0553108174253549,
>>>>
>>>> -0.0548340548340548, -0.0546601261387525, -0.054590570719603,
>>>>
>>>> -0.0545001187366422, -0.0544511668107173, -0.0544274300932089,
>>>>
>>>> -0.0542372881355932, -0.0542168674698794, -0.0540540540540541,
>>>>
>>>> -0.053763440860215, -0.0537513997760358, -0.0536343468615424,
>>>>
>>>> -0.0535714285714286, -0.0534725518114223, -0.0529294274300931,
>>>>
>>>> -0.0528846153846155, -0.0528756957328386, -0.0526458340386634,
>>>>
>>>> -0.0526315789473684, -0.0525606469002696, -0.0525451559934318,
>>>>
>>>> -0.0525227460711332, -0.051948051948052, -0.051792828685259,
>>>>
>>>> -0.0517241379310345, -0.0513784461152881, -0.0513559322033898,
>>>>
>>>> -0.0512610211195407, -0.0512437810945274, -0.051150895140665,
>>>>
>>>> -0.0510695486616643, -0.0507726269315673, -0.0507377685736475,
>>>>
>>>> -0.0506575742815391, -0.0506024096385543, -0.0505494505494506,
>>>>
>>>> -0.0503194888178913, -0.0501567398119122, -0.05, -0.0499001996007984,
>>>>
>>>> -0.0498214285714285, -0.0497737556561087, -0.0497470489038785,
>>>>
>>>> -0.0494845360824741, -0.0493827160493827, -0.0492157923201731,
>>>>
>>>> -0.0491192897035657, -0.0489642184557439, -0.0488200324265898,
>>>>
>>>> -0.0488031366075114, -0.0485151426051161, -0.0483319076133448,
>>>>
>>>> -0.0481220657276996, -0.0480897675661234, -0.0480599647266314,
>>>>
>>>> -0.0480038022813688, -0.0479900280461202, -0.0479548660084627,
>>>>
>>>> -0.0478449164776243, -0.0475638051044084, -0.0475342709631477,
>>>>
>>>> -0.0473213579172271, -0.0472997462848857, -0.0472050636772667,
>>>>
>>>> -0.046890780551147, -0.0467625899280576, -0.046753107010276,
>>>>
>>>> -0.0466592011944754, -0.0465772759350741, -0.0465753424657535,
>>>>
>>>> -0.0464333781965007, -0.0463888365076373, -0.0463215258855587,
>>>>
>>>> -0.046281851274051, -0.0459946060208471, -0.0458715596330275,
>>>>
>>>> -0.0458563535911603, -0.0457367549668873, -0.0456500165398611,
>>>>
>>>> -0.0454373701114679, -0.0454265548766046, -0.0454183266932271,
>>>>
>>>> -0.045213508233324, -0.045182571340902, -0.0451018428709989,
>>>>
>>>> -0.0451018428709989, -0.044955044955045, -0.0444136016655101,
>>>>
>>>> -0.0443722943722945, -0.0442996742671011, -0.0442477876106195,
>>>>
>>>> -0.0442477876106195, -0.0441176470588236, -0.043982895540623,
>>>>
>>>> -0.0438184663536776, -0.0436363636363636, -0.043261231281198,
>>>>
>>>> -0.0432218514782339, -0.0431654676258993, -0.0424336600525938,
>>>>
>>>> -0.0423429781227946, -0.0423387096774193, -0.0420711974110032,
>>>>
>>>> -0.0420083118050095, -0.0420032310177707, -0.0417256011315418,
>>>>
>>>> -0.0416842105263158, -0.0416141235813367, -0.0414593698175788,
>>>>
>>>> -0.0413793103448276, -0.041320942582144, -0.0407865986890023,
>>>>
>>>> -0.0406158747013539, -0.0405803571428572, -0.0405643738977073,
>>>>
>>>> -0.040422053796998, -0.040268456375839, -0.0400500625782228,
>>>>
>>>> -0.0400449101796407, -0.04, -0.0399718147460123, -0.0399137001078749,
>>>>
>>>> -0.0399044464954666, -0.0398863290368415, -0.0398230088495575,
>>>>
>>>> -0.0394736842105263, -0.0393401015228426, -0.0392720306513411,
>>>>
>>>> -0.0392156862745098, -0.0388349514563106, -0.0386904761904763,
>>>>
>>>> -0.0384615384615385, -0.0382457345700217, -0.0382293762575454,
>>>>
>>>> -0.0381840048105834, -0.0380030474141795, -0.0379746835443038,
>>>>
>>>> -0.0379247280777747, -0.0376432078559739, -0.0375494071146245,
>>>>
>>>> -0.0375490837696336, -0.0373345788572318, -0.0372940156114484,
>>>>
>>>> -0.0371871275327772, -0.037037037037037, -0.0368133174791915,
>>>>
>>>> -0.0368098159509203, -0.0367231638418078, -0.0361445783132531,
>>>>
>>>> -0.0360915492957746, -0.0357142857142857, -0.0356663184599313,
>>>>
>>>> -0.0356413696552528, -0.035513103110458, -0.0353194103194103,
>>>>
>>>> -0.0352112676056338, -0.0350119904076739, -0.0349794238683129,
>>>>
>>>> -0.0349373764007909, -0.0349091600875106, -0.0347826086956522,
>>>>
>>>> -0.0347728547392037, -0.0347682119205298, -0.0346083788706739,
>>>>
>>>> -0.0344706296166022, -0.0344421548425081, -0.0341176470588236,
>>>>
>>>> -0.0338983050847458, -0.033457249070632, -0.0334208223972004,
>>>>
>>>> -0.0333333333333334, -0.0333333333333333, -0.0329670329670331,
>>>>
>>>> -0.0329144225014961, -0.0326797385620915, -0.0323033707865168,
>>>>
>>>> -0.0322118826055834, -0.0321750321750322, -0.0320890635232481,
>>>>
>>>> -0.0318302387267905, -0.0316666666666666, -0.0315586914688903,
>>>>
>>>> -0.0312606184165817, -0.030881017257039, -0.0308764940239045,
>>>>
>>>> -0.0305419952434597, -0.030406198638178, -0.0299651567944252,
>>>>
>>>> -0.029945999018164, -0.0298786181139121, -0.0295741147960329,
>>>>
>>>> -0.0293917033546227, -0.029171528588098, -0.0291327913279132,
>>>>
>>>> -0.0290497291974397, -0.0288721376760064, -0.0287704170466792,
>>>>
>>>> -0.0286236297198539, -0.0285714285714286, -0.0277575837684224,
>>>>
>>>> -0.0277085471338513, -0.0275897304892068, -0.0275526742301458,
>>>>
>>>> -0.027027027027027, -0.0270270270270269, -0.0269087523277468,
>>>>
>>>> -0.0268918695148203, -0.02676704307821, -0.026454253142356,
>>>> -0.0263157894736842,
>>>>
>>>> -0.0263157894736842, -0.0261660978384529, -0.025974025974026,
>>>>
>>>> -0.0257503107796129, -0.0255319148936171, -0.0254237288135594,
>>>>
>>>> -0.025297619047619, -0.0249174422095467, -0.0248888888888889,
>>>>
>>>> -0.024767619719967, -0.0246053853296194, -0.0245269796776454,
>>>>
>>>> -0.024390243902439, -0.0241935483870968, -0.0238907849829351,
>>>>
>>>> -0.0238153295944078, -0.0234413496961306, -0.0232558139534884,
>>>>
>>>> -0.0232558139534883, -0.0230392156862745, -0.0230360307147077,
>>>>
>>>> -0.0228847365106026, -0.0225806451612903, -0.0224519940915805,
>>>>
>>>> -0.0214786344110332, -0.0212360867018161, -0.0205245153933865,
>>>>
>>>> -0.0204170602339606, -0.0200986321764215, -0.0200729927007299,
>>>>
>>>> -0.0199828473413379, -0.0194174757281553, -0.0193536931818183,
>>>>
>>>> -0.0192885771543086, -0.019222732971166, -0.0191414840759143,
>>>>
>>>> -0.0189573459715641, -0.0188902007083826, -0.0186903321231681,
>>>>
>>>> -0.0184456468273487, -0.0183066361556064, -0.0182166826462128,
>>>>
>>>> -0.0181149908112366, -0.0179372197309418, -0.0179172441100772,
>>>>
>>>> -0.0178571428571429, -0.0174672489082969, -0.0174216027874564,
>>>>
>>>> -0.0171428571428572, -0.017017253604349, -0.0169252468265163,
>>>>
>>>> -0.0165094339622642, -0.0158730158730158, -0.0158415841584159,
>>>>
>>>> -0.0157247037374659, -0.0157089706490286, -0.0156250000000001,
>>>>
>>>> -0.0153846153846153, -0.0151668351870576, -0.0151589242053789,
>>>>
>>>> -0.0150489089541008, -0.0150262202501008, -0.0150081124932396,
>>>>
>>>> -0.0148196281468128, -0.0144251166737377, -0.0142857142857142,
>>>>
>>>> -0.0140638734251392, -0.0136986301369863, -0.0133333333333333,
>>>>
>>>> -0.0129464285714286, -0.0129449838187702, -0.0127813811522321,
>>>>
>>>> -0.0126030053320408, -0.0125721665147373, -0.0125, -0.0122160435399906,
>>>>
>>>> -0.0122116689280869, -0.0121019108280255, -0.0118747750989563,
>>>>
>>>> -0.0118277953189996, -0.0117107942973524, -0.0115172759138707,
>>>>
>>>> -0.0114087997381585, -0.0113924050632912, -0.0111524163568772,
>>>>
>>>> -0.0111248454882571, -0.0111111111111111, -0.0102570933795125,
>>>>
>>>> -0.0102040816326532, -0.00963463463463469, -0.00958657878969439,
>>>>
>>>> -0.00941028858218319, -0.00874453466583389, -0.00779588944011335,
>>>>
>>>> -0.00713620850139625, -0.00710720027075056, -0.00709219858156026,
>>>>
>>>> -0.00624999999999998, -0.00551977920883173, -0.00521499557217353,
>>>>
>>>> -0.00453998797354176, -0.00444444444444444, -0.00166389351081533,
>>>>
>>>> -0.00118483412322285, -0.00100704934541787, -0.000937500000000036,
>>>>
>>>> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
>>>>
>>>> 0.000218031178458569, 0.000796495420151402, 0.00167130919220062,
>>>>
>>>> 0.00190476190476193, 0.00350058343057173, 0.00363914958820145,
>>>>
>>>> 0.00432900432900424, 0.00456037942356804, 0.00477446915441642,
>>>>
>>>> 0.0050825509873745, 0.00525691029336935, 0.00603318250377083,
>>>>
>>>> 0.00652173913043472, 0.00733192494097176, 0.00747663551401869,
>>>>
>>>> 0.00760456273764256, 0.00812529439472442, 0.00991231414410967,
>>>>
>>>> 0.0101685066821615, 0.0106182565507793, 0.0109070034443169,
>>>> 0.0115183246073298,
>>>>
>>>> 0.0115442244823827, 0.0127659574468085, 0.0128076846107665,
>>>> 0.0135135135135135,
>>>>
>>>> 0.0140845070422535, 0.0150730098916627, 0.0159362549800796,
>>>> 0.0172413793103449,
>>>>
>>>> 0.0176899063475547, 0.0186954715413378, 0.0187765706188003,
>>>> 0.0195757403189066,
>>>>
>>>> 0.019607843137255, 0.0199999999999999, 0.0210526315789473,
>>>> 0.0221979621542939,
>>>>
>>>> 0.0239410681399632, 0.0239999999999999, 0.025149051490515,
>>>> 0.0260869565217392,
>>>>
>>>> 0.0262475696694749, 0.028180542563143, 0.0285714285714286,
>>>> 0.0303030303030302,
>>>>
>>>> 0.0315904139433552, 0.0341864716636198, 0.0375782881002089,
>>>> 0.038479809976247,
>>>>
>>>> 0.0387596899224806, 0.0416666666666667, 0.0428100987925357,
>>>> 0.0428134556574923,
>>>>
>>>> 0.0437201907790144, 0.0451127819548872, 0.0460251046025105,
>>>> 0.0487779511180447,
>>>>
>>>> 0.048975188781014, 0.0529872938632063, 0.0562390158172233,
>>>> 0.0589335827876521,
>>>>
>>>> 0.0617551462621885, 0.0628115653040877, 0.0671812464265294,
>>>> 0.0721784776902887,
>>>>
>>>> 0.0736842105263157, 0.0833333333333334, 0.083862394802894,
>>>> 0.0970464135021097,
>>>>
>>>> 0.0971168437025795, 0.102272727272727, 0.111111111111111,
>>>> 0.117117117117117,
>>>>
>>>> 0.123532699832309, 0.141304347826087, 0.179487179487179,
>>>> 0.191268191268191,
>>>>
>>>> 0.205128205128205, 0.219020172910663, 0.271590909090909,
>>>> 0.333333333333333
>>>>
>>>> )
>>>>
>>>>
>>>> Now I want to estimate empirical PDF for interval of (-1, 1) including
>>>> all points of Dat
>>>>
>>>> I have looked into the density() function, however it appears that,
>>>> empirical density is estimated for equally distant points, which not
>>>> necessarily contains actual supplied points (in my case, Dat)
>>>>
>>>> Is there any option to achieve the same?
>>>>
>>>> Thanks for your pointer.
>>>>
>>>> ______________________________________________
>>>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>>> PLEASE do read the posting guide
>>>> http://www.R-project.org/posting-guide.html
>>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>>
>>
>> ______________________________________________
>> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

---------------------------------------------------------------------------
Jeff Newmiller                        The     .....       .....  Go Live...
DCN:<[hidden email]>        Basics: ##.#.       ##.#.  Live Go...
                                       Live:   OO#.. Dead: OO#..  Playing
Research Engineer (Solar/Batteries            O.O#.       #.O#.  with
/Software/Embedded Controllers)               .OO#.       .OO#.  rocks...1k

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.