Re: Beta distribution

[Ben Pfaff]

John Darrington <address@hidden> writes:

> Some of the values which are causing problems aren't particularly
> extreme.
>
> I'm suspecting a problem with lib/gsl_extras/betadistinv.c
>   
> In particular  gslextras_cdf_beta_Pinv.

I have output for the same test when run with SPSS 12.0 on a
Windows machine.  The diff against f.out produced by SPSS 12.0
versus the values in the PSPP tests directory looks like this:

85c85
<       .50     2.00     1.00     1.50      .50      .13 
---
>      .50     2.00     1.00     1.50      .50      .12 
98c98
<       .60     1.00     2.00     1.13      .60      .17 
---
>      .60     1.00     2.00     1.12      .60      .17 
101c101
<       .60     2.00     1.00     2.62      .60      .06 
---
>      .60     2.00     1.00     2.63      .60      .06 
172c172
<       .99     5.00    10.00     5.64      .99      .01 
---
>      .99     5.00    10.00    10.00     1.00      .00 

(The columns are:
        P       df1     df2       i         c        p
 where i = idf.f(P, df1, df2),
       c = cdf.f(i, df1, df2),
   and p = pdf.f(i, df1, df2).)

Only a few values are off.  The only one off by much is the
example you pointed out.  A similar diff for the beta
distribution looks like this:

211c211
<       .99      .75      .25     1.00      .99 164383.5 
---
>      .99      .75      .25     1.00      .98 20860.76 
218c218
<       .99     1.00      .25     1.00      .99 250000.0 
---
>      .99     1.00      .25     1.00      .98 46067.00 
225c225
<       .99     1.50      .25     1.00      .99 431322.3 
---
>      .99     1.50      .25     1.00      .98 67836.74 

(The columns are:
        P         a       b       i         c        p
 where i = idf.beta(P, a, b),
       c = cdf.beta(i, a, b),
   and p = pdf.beta(i, a, b).)

Here, only the extreme values are off as far as I can tell.  I
suppose this must be the root of the problem though.

(This is a good part of what I was going to bring up with Jason
anyhow.)
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--Bruce Schneier