Thanks for your interest. An issue that recently came up in the Probability
module is sampling from a Poisson distribution
<https://en.wikipedia.org/wiki/Poisson_distribution>. It used to not work
at all, and now it does but the algorithm is not efficient when the
parameter lamda is large. For example:
from sympy.stats import *
sample(Poisson('x', 1000))
can take a while to return.
Usually one can sample by generating a Uniform(0, 1) random number u, and
then apply the inverse of the cumulative distribution function (CDF) to u.
But there isn't a formula for the inverse of the of a Poisson random
variable. The current algorithm
<https://github.com/sympy/sympy/blob/master/sympy/stats/drv_types.py#L31>
simply
goes over all integers looking for the first one where CDF(n) >= u. There
ought to be a better way of doing this.
The first idea that comes to mind is to make giant steps (in power of 2)
until CDF(n) >= u is reached, and then refine by bisection. But perhaps
it's better to do research first, there is probably an algorithm out there
that we can use. Maybe R has it? https://www.r-project.org/
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