Re: [Rd] An extreme quantile of the geometric distribution

From: peter dalgaard <pdalgd_at_gmail.com>
Date: Sat, 30 Jun 2012 16:15:13 +0200

On Jun 30, 2012, at 12:13 , <michael.baudin_at_contrib.scilab.org> <michael.baudin_at_contrib.scilab.org> 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 <pdalgd_at_gmail.com> wrote:

>> On Jun 28, 2012, at 22:49 , <michael.baudin_at_contrib.scilab.org>
>> <michael.baudin_at_contrib.scilab.org> 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
>>> 
>>> ______________________________________________
>>> R-devel_at_r-project.org 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: (+45)38153501
Email: pd.mes_at_cbs.dk  Priv: PDalgd_at_gmail.com

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