# Thread: Proof CDF for Poisson distribution

1. ## Proof CDF for Poisson distribution

Hello,
How can proof and write CDF for Poisson distribution?
(Later: I need CDF for Poisson distribution to generate random number.)

2. ## Re: Proof CDF for Poisson distribution

The usual (not always the best for large $\lambda$) way of generating Poisson distributes psuedo random numbers is to use Knuth's algorithm.

Psuedo-code for this is shwn below:

Code:
function PRN(lambda)
% -------------------------------------------------------------
% Generate a random value from the (discrete) Poisson
% distribution with parameter lambda, using Knuth's Algorithm.
%
% See pages 132-3 of v2 TAOCP, Semi-Numerical Algorithms 2nd Ed. Don Knuth 1981.
%
%--------------------------------------------------------------
k=0;prod=UniformRand;
repeat
if prod<=exp(-lambda)
break
endif
prod=prod*UniformRand;
k=k+1;
end
return k
endfunction

3. ## Re: Proof CDF for Poisson distribution

Hey life24.

The proof for a Poisson distribution is based on taking a Binomial distribution and finding out what happens when you have an infinite number of trials before converting it to a rate process [instead of a counting process].

https://en.wikipedia.org/wiki/Poisson_distribution

Try taking a binomial distribution, send the count to infinity and normalize it so that you get a rate instead of a count.