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## Density estimate with bounds

 Dear R users, I would like to show the estimated density of a (0, 1) uniformly distributed random variable. The density curve, however, goes beyond 0 and 1 because of the kernel smoothing. Example: x = runif(10000) plot(density(x)) Is there a way to estimate the density curve strictly within (0, 1) and still use some sort of smoothing? Any help would be greatly appreciated. Best regards, Justine Rochon ________________________ Justine Rochon - Biostatistician - Center for Clinical Studies University Hospital Regensburg Franz-Josef-Strauß-Allee 11 D-93053 Regensburg Phone: ++49-(0)941-944-5626 Fax: ++49-(0)941-944-5632 Email: [hidden email] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Density estimate with bounds

 On 05/11/2009 4:35 AM, Justine Rochon wrote: > Dear R users, > > I would like to show the estimated density of a (0, 1) uniformly distributed > random variable. The density curve, however, goes beyond 0 and 1 because of the > kernel smoothing. > > Example: > > x = runif(10000) > plot(density(x)) > > Is there a way to estimate the density curve strictly within (0, 1) and still > use some sort of smoothing? > > Any help would be greatly appreciated. One way is to extend the data by reflection on each end.  That is, x <- runif(10000) ex_x <- c(-x, x, 2-x) den <- density(ex_x) plot(den\$x, 3*den\$y, xlim=c(0,1), type="l") You need the rescaling to 3*den\$y because you've tripled the range. Duncan Murdoch ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Antw: Re: Density estimate with bounds

 Hi Duncan, Thank you for your e-mail. It works for the uniform distribution, but I have trouble with the exponential distribution: x <- rexp(10000) ex_x <- c(-x, x) den <- density(ex_x) plot(den\$x, 2*den\$y, xlim=c(0,5), type="l") Best regards, Justine ________________________ Justine Rochon - Biostatistician - Center for Clinical Studies University Hospital Regensburg Franz-Josef-Strauß-Allee 11 D-93053 Regensburg Phone: ++49-(0)941-944-5626 Fax: ++49-(0)941-944-5632 Email: [hidden email]     >>> Duncan Murdoch <[hidden email]> 05.11.2009 12:36 >>> On 05/11/2009 4:35 AM, Justine Rochon wrote: > Dear R users, > > I would like to show the estimated density of a (0, 1) uniformly distributed > random variable. The density curve, however, goes beyond 0 and 1 because of the > kernel smoothing. > > Example: > > x = runif(10000) > plot(density(x)) > > Is there a way to estimate the density curve strictly within (0, 1) and still > use some sort of smoothing? > > Any help would be greatly appreciated. One way is to extend the data by reflection on each end.  That is, x <- runif(10000) ex_x <- c(-x, x, 2-x) den <- density(ex_x) plot(den\$x, 3*den\$y, xlim=c(0,1), type="l") You need the rescaling to 3*den\$y because you've tripled the range. Duncan Murdoch ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.
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## Re: Antw: Re: Density estimate with bounds

 On 11/5/2009 8:36 AM, Justine Rochon wrote: > Hi Duncan, > > Thank you for your e-mail. > > It works for the uniform distribution, but I have trouble with the exponential > distribution: > > x <- rexp(10000) > ex_x <- c(-x, x) > den <- density(ex_x) > plot(den\$x, 2*den\$y, xlim=c(0,5), type="l") Just don't plot the out-of-range values.  For example, keep <- den\$x >= 0 plot(den\$x[keep], 2*den\$y[keep], type="l") It doesn't do a good job of estimating the density right near zero; for that, you'd need to pre-transform to get it flat, then transform back. For example, if you knew it was like an exponential near zero, you could do the following: u <- 1-exp(-x)  # transform to uniform u <- c(-u, u)   # reflect x <- -log(1-u)  # transform back If you get the scale wrong (i.e. it isn't Exp(1), but it is like some other exponential near zero), this should still be okay if you're close or you have lots of data.  If you are way off (e.g. some other shape of gamma distribution) it won't work well at all. Duncan Murdoch > > Best regards, > > Justine > > > > > > > ________________________ > Justine Rochon > - Biostatistician - > Center for Clinical Studies > University Hospital Regensburg > Franz-Josef-Strauß-Allee 11 > D-93053 Regensburg > Phone: ++49-(0)941-944-5626 > Fax: ++49-(0)941-944-5632 > Email: [hidden email] >   >   >>>> Duncan Murdoch <[hidden email]> 05.11.2009 12:36 >>> > On 05/11/2009 4:35 AM, Justine Rochon wrote: >> Dear R users, >> >> I would like to show the estimated density of a (0, 1) uniformly > distributed >> random variable. The density curve, however, goes beyond 0 and 1 because of > the >> kernel smoothing. >> >> Example: >> >> x = runif(10000) >> plot(density(x)) >> >> Is there a way to estimate the density curve strictly within (0, 1) and > still >> use some sort of smoothing? >> >> Any help would be greatly appreciated. > > One way is to extend the data by reflection on each end.  That is, > > x <- runif(10000) > ex_x <- c(-x, x, 2-x) > den <- density(ex_x) > plot(den\$x, 3*den\$y, xlim=c(0,1), type="l") > > You need the rescaling to 3*den\$y because you've tripled the range. > > Duncan Murdoch ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.