Re: Error in evaluating Poisson CDF

[Peter Johansson]

Hi Sebastiano,

On 8/2/21 9:00 am, Sebastiano Vigna wrote:
> This program
>
> #include <gsl/gsl_cdf.h>
> #include <stdio.h>
> int main() {
>          printf("%f\n", gsl_cdf_poisson_Q(7165697, 7168929.393553));
> }

As a workaround you could use the fact that for large m, Poisson(x, m) 
is approximately Gaussian(x, m, sigma=sqrt(m)), so something like 
gsl_cdf_gaussian_Q( 7168929.393553 - 7165697, sqrt(7165697))

hope that helps,


Peter


> prints
>
> gsl: gamma_inc.c:181: ERROR: error in large x asymptotic
> Default GSL error handler invoked.
> Aborted (core dumped)
>
> on gsl 2.6 (Fedora Linux). scipy, for instance, has no problem in evaluating it:
>
> > > > scipy.stats.poisson.sf(7165697, 7168929.393553);
> 0.8863015162515768
>
> This kind of error is reported a bit randomly with certain large parameters 
> (I'm running a large number of collision tests for PRNGs, and the distribution 
> of collisions is approximated by a Poisson distribution, so I'm evaluating a 
> lot of those with different parameters). I can provide more examples if this is 
> useful in understanding the problem.
>
> Ciao,
>
>                                         seba