Re: [boost] [random] poisson_distribution problem and fix

From: Topher Cooper (topher_at_[hidden])
Date: 2007-12-27 11:03:39

At 02:26 PM 12/26/2007, I wrote:

>I was implying (when I should have been saying) that at some point
>the error of generating a *normal* random variant with a mean and
>standard deviate of lambda instead of a "for real" Poisson becomes
>too small to have any practical significance.  If large lambdas are
>causing problems then one solution is to see if this is only
>occurring sufficiently far into that regime then it might make sense
>to just generate a normal instead.  Scaling and shifting by 750 is
>not likely to cause much rounding errors for a standard normal
>deviate, but many direct algorithms for that extreme a value are
>likely to run into numerical problems.
>
>Topher

I checked this out.  The difference between the two curves 
(Poisson[750] and Normal[750, Sqrt(750)]) is very small -- when 
plotted, almost indistinguishable to the eye.  In total, the absolute 
difference between the two is about 1%.  The largest single error was 
that using the normal generator would result in 729 being generated 
with a probability of 0.01086
  instead of 0.01098.  While that is unlikely to have much effect on 
most applications, it is possible that a large simulation that is 
very sensitive to the precise probabilities might be thrown off, so I 
withdraw this suggestion.

Topher