Page 116 - Computational Statistics Handbook with MATLAB

Chapter 4: Generating Random Variables 103

This leads to the following algorithm.

PROCEDURE - GENERATING POISSON RANDOM VARIABLES

1. Generate a uniform random number U.
2. Initialize the quantities: i = 0 , p 0 = e – λ , and F 0 = p 0 .
3. If U ≤ F i , then deliver X = i . Return to step 1.
4. Else increment the values: p i + = λp i (⁄ i + 1) , i = i + 1 , and
1
F i + = F i + p i + 1 .
1
5. Return to step 3.
λ
This algorithm could be made more efficient when is large. The interested
reader is referred to Ross [1997] for more details.

Example 4.13
The following shows how to implement the procedure for generating Pois-
son random variables in MATLAB.
% function X = cspoirnd(lam,n)
% This function will generate Poisson
% random variables with parameter lambda.
% The reference for this is Ross, 1997, page 50.

function x = cspoirnd(lam,n)
x = zeros(1,n);
j = 1;
while j <= n
flag = 1;
% initialize quantities
u = rand(1);
i = 0;
p = exp(-lam);
F = p;
while flag % generate the variate needed
if u <= F % then accept
x(j) = i;
flag = 0;
j = j+1;
else % move to next probability
p = lam*p/(i+1);
i = i+1;
F = F + p;
end
end

© 2002 by Chapman & Hall/CRC