Random variable from pdf in matlab

Question

I want to simulate some random variables distributed as a Variance Gamma.

I know the pdf ( http://en.wikipedia.org/wiki/Variance-gamma_distribution ) but I don't know the inverse of the cumulative function F: so I can't generate a random uniform variable U and compute x=F^(-1)(U). I have to do this in MATLAB.

Thank you!

Stefano

Answer 1

The next natural alternative to look into is Von Neumann's "acceptance-rejection method".

If you can find a density g defined on the same space as your f such that

1. you know how to generate samples from g , and
2. f(x) <= cg(x), for some c, for all x,

then you are good to go.

If you search the literature, people must have done this. The VG is widely used in pricing options.

Answer 2

Following @Drake 's idea: for the first step you can use Marsaglia and Tsang's Method from here .

This is the code to generate gamma random numbers:

function x=gamrand(alpha,lambda)
% Gamma(alpha,lambda) generator using Marsaglia and Tsang method
% Algorithm 4.33
if alpha>1
    d=alpha-1/3; c=1/sqrt(9*d); flag=1;
    while flag
        Z=randn;
        if Z>-1/c
            V=(1+c*Z)^3; U=rand;
            flag=log(U)>(0.5*Z^2+d-d*V+d*log(V));
        end
    end
    x=d*V/lambda;
else
    x=gamrand(alpha+1,lambda);
    x=x*rand^(1/alpha);
end