An extreme quantile of the geometric distribution

[michael.baudin]

 Hi,

 With R version 2.10.0 (2009-10-26) on Windows, I computed the p=1.e-20
 quantile of the geometric distribution with parameter prob=0.1.

> qgeom(1.e-20,0.1)
 [1] -1

 But this is not possible, since X=0,1,2,...

 I guess that this might be a bug in the quantile function, which should
 use the log1p function, instead of the naive formula.

 Am I correct ?

 Best regards,

 Michaël

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[Peter Dalgaard-2]

On Jun 28, 2012, at 22:49 , <[hidden email]> <[hidden email]> wrote:

> Hi,
>
> With R version 2.10.0 (2009-10-26) on Windows, I computed the p=1.e-20 quantile of the geometric distribution with parameter prob=0.1.
>
>> qgeom(1.e-20,0.1)
> [1] -1
>
> But this is not possible, since X=0,1,2,...
>
> I guess that this might be a bug in the quantile function, which should use the log1p function, instead of the naive formula.
>
> Am I correct ?

Nope. (The source is availably, you know....).

The problem is that a slight fuzz is subtracted inside ceil(....), but there's no check that the result is positive.

qnbinom(...., size=1) is equivalent and does get right, by the way.  

-pd

>
> Best regards,
>
> Michaël
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-devel

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: [phone]
Email: [hidden email]  Priv: [hidden email]

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[michael.baudin]

 Hi,

 I'm sorry, I do not clearly understand.

 I'm aware that the source is available at :

 http://svn.r-project.org/R/trunk/src/nmath/qgeom.c

 But a good source does not mean a correct result, because of
 compilation issues. Moreover, I do not fully understand why the 1e-7
 coefficient in the formula was put there. The comment "add a fuzz to
 ensure left continuity" is not obvious to me.

 Best regards,

 Michaël

 On Fri, 29 Jun 2012 14:21:50 +0200, peter dalgaard <[hidden email]>
 wrote:

> On Jun 28, 2012, at 22:49 , <[hidden email]>
> <[hidden email]> wrote:
>
>> Hi,
>>
>> With R version 2.10.0 (2009-10-26) on Windows, I computed the
>> p=1.e-20 quantile of the geometric distribution with parameter
>> prob=0.1.
>>
>>> qgeom(1.e-20,0.1)
>> [1] -1
>>
>> But this is not possible, since X=0,1,2,...
>>
>> I guess that this might be a bug in the quantile function, which
>> should use the log1p function, instead of the naive formula.
>>
>> Am I correct ?
>
> Nope. (The source is availably, you know....).
>
> The problem is that a slight fuzz is subtracted inside ceil(....),
> but there's no check that the result is positive.
>
> qnbinom(...., size=1) is equivalent and does get right, by the way.
>
> -pd
>
>>
>> Best regards,
>>
>> Michaël
>>
>> ______________________________________________
>> [hidden email] mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel

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[Peter Dalgaard-2]

On Jun 30, 2012, at 12:13 , <[hidden email]> <[hidden email]> wrote:

> Hi,
>
> I'm sorry, I do not clearly understand.
>
> I'm aware that the source is available at :
>
> http://svn.r-project.org/R/trunk/src/nmath/qgeom.c

Yes, but you were suggesting that non-use of log1p caused the problem, and the source clearly uses it, so I assumed that you didn't check.

>
> But a good source does not mean a correct result, because of compilation issues. Moreover, I do not fully understand why the 1e-7 coefficient in the formula was put there. The comment "add a fuzz to ensure left continuity" is not obvious to me.

I never implied that there wasn't a problem.

The gist of the comment it is that we want to ensure that (for moderate i at least)

qgeom(pgeom(i,.1),.1)==i

and that slightly lower values should also give i, whereas higher values give i+1:

> qgeom(pgeom(1,.1),.1)
[1] 1
> qgeom(pgeom(1,.1)-.01,.1)
[1] 1
> qgeom(pgeom(1,.1)+.01,.1)
[1] 2

However, floating point calculations being what they are, we don't trust equality, so we move the cutpoint a little -- apparently a little too much.

> Best regards,
>
> Michaël
>
> On Fri, 29 Jun 2012 14:21:50 +0200, peter dalgaard <[hidden email]> wrote:
>> On Jun 28, 2012, at 22:49 , <[hidden email]>
>> <[hidden email]> wrote:
>>
>>> Hi,
>>>
>>> With R version 2.10.0 (2009-10-26) on Windows, I computed the p=1.e-20 quantile of the geometric distribution with parameter prob=0.1.
>>>
>>>> qgeom(1.e-20,0.1)
>>> [1] -1
>>>
>>> But this is not possible, since X=0,1,2,...
>>>
>>> I guess that this might be a bug in the quantile function, which should use the log1p function, instead of the naive formula.
>>>
>>> Am I correct ?
>>
>> Nope. (The source is availably, you know....).
>>
>> The problem is that a slight fuzz is subtracted inside ceil(....),
>> but there's no check that the result is positive.
>>
>> qnbinom(...., size=1) is equivalent and does get right, by the way.
>>
>> -pd
>>
>>>
>>> Best regards,
>>>
>>> Michaël
>>>
>>> ______________________________________________
>>> [hidden email] mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-devel

--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: [phone]
Email: [hidden email]  Priv: [hidden email]

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