random numbers from custom mixture distribution

I would like to generate random numbers from a mixture distribution defined as,

pdf_mix = p*gampdf(x,a,b) + (1-p)*lognpdf(x,mu,sigma);

I am able to obtain the best fit model using mle, but I also want random numbers generated from this mixture distribution. Is this possible? Can I get some help on this?

R Venkatessh

Answer 1

[Roger Stafford]

Here's another method you might consider that would allow you to directly use the 'gamrnd' and 'lognrnd' functions in the Statistics Toolbox. Suppose you want an m by n matrix, R, of random values in accordance with your mixed distribution.

 U = rand(m,n)<=p; % U is true with probability p and false with probability 1-p
 R = U.*gamrnd(a,b,m,n)+(1-U).*lognrnd(mu,sigma,m,n);

R should have the desired distribution.

Answer 2

[Image Analyst]

Calculate the CDF and then get a random number from the uniform distribution and plug it in. See the method described here: http://en.wikipedia.org/wiki/Inverse_transform_sampling I've also attached my program for doing it with a rayleigh distribution. Click on the filename below (not the picture, but the filename).