Re: bug in gsl_ran_chisq_pdf

Re: bug in gsl_ran_chisq_pdf

[Rodney Sparapani]

>On Tue, 8 Apr 2003 keith.briggs@bt.com wrote:
>
>> In gsl-1.3, gsl_ran_chisq_pdf(0.0,nu) is wrong.
>>
>> It returns 0.0 whatever nu is.
>
>That seems to be the default behavior, absent the indication of a
>domain error.  The Gamma pdf on x requires x > 0, so it does make some
>sense to return 0 for any x outside the defined domain.
>
>You seem to be suggesting that the limit for x->0 from above be
>returned instead.
>
>> It should return Inf for nu=1.
>> It should return 0.5 for nu=2.
>> It should return 0.0 for nu>2.
>
>The parameter nu is declared double, so your suggestion is not
>exhaustive.  You probably meant to say
>
>  raise an error for nu <= 0
>  return Inf for 0 < nu < 2
>  return 0.5 for nu == 2
>  return 0.0 for nu > 2
>
>Anyway, I haven't seen an explicit statement about the desired
>behavior of the _pdf functions when the main argument is outside the
>domain of definition.  Personally, I find the currently implemented
>behavior reasonable: the univariate PDFs in GSL are defined on
>single intervals, and the _pdf functions return 0 for values outside
>the interval (the _cdf functions would have to return 0 below the
>defined interval and 1 above).
>
>- martin

Fascinating discussion.  However, the foundation of the Chi-square distribution 
should follow from the sum of squared, independent standard Normals rather than 
a special case of the Gamma distribution.  If that's the case, then the 
Chi-square pdf is defined at 0; for example, see Kendall's Advanced Theory of 
Statistics, Volume I:  Distribution Theory.  By the way, I think the previous 
correspondents are neglecting the term 1/sqrt(pi).  

Rodney Sparapani              Medical College of Wisconsin
Sr. Biostatistician           Patient Care & Outcomes Research
rsparapa@mcw.edu              http://www.mcw.edu/pcor
Was 'Name That Tune' rigged?  WWLD -- What Would Lombardi Do

Re: bug in gsl_ran_chisq_pdf

[Brian Gough]

Martin Jansche writes:
 > Anyway, I haven't seen an explicit statement about the desired
 > behavior of the _pdf functions when the main argument is outside the
 > domain of definition.  Personally, I find the currently implemented
 > behavior reasonable: the univariate PDFs in GSL are defined on
 > single intervals, and the _pdf functions return 0 for values outside
 > the interval (the _cdf functions would have to return 0 below the
 > defined interval and 1 above).

I have in mind,
 
return 0 outside valid range (as currently)
return NaN for invalid parameters (not actually implemented)

Re: bug in gsl_ran_chisq_pdf

[Martin Jansche]

On Tue, 8 Apr 2003 keith.briggs@bt.com wrote:

> In gsl-1.3, gsl_ran_chisq_pdf(0.0,nu) is wrong.
>
> It returns 0.0 whatever nu is.

That seems to be the default behavior, absent the indication of a
domain error.  The Gamma pdf on x requires x > 0, so it does make some
sense to return 0 for any x outside the defined domain.

You seem to be suggesting that the limit for x->0 from above be
returned instead.

> It should return Inf for nu=1.
> It should return 0.5 for nu=2.
> It should return 0.0 for nu>2.

The parameter nu is declared double, so your suggestion is not
exhaustive.  You probably meant to say

  raise an error for nu <= 0
  return Inf for 0 < nu < 2
  return 0.5 for nu == 2
  return 0.0 for nu > 2

Anyway, I haven't seen an explicit statement about the desired
behavior of the _pdf functions when the main argument is outside the
domain of definition.  Personally, I find the currently implemented
behavior reasonable: the univariate PDFs in GSL are defined on
single intervals, and the _pdf functions return 0 for values outside
the interval (the _cdf functions would have to return 0 below the
defined interval and 1 above).

- martin

bug in gsl_ran_chisq_pdf

[keith.briggs]

In gsl-1.3, gsl_ran_chisq_pdf(0.0,nu) is wrong.

It returns 0.0 whatever nu is.

It should return Inf for nu=1.
It should return 0.5 for nu=2.
It should return 0.0 for nu>2.

Keith

	Dr. Keith M. Briggs
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