How to create a Rician random variable?

Question

I\'m trying to model a signal detection problem using Sympy, and need two random variables. One with a Rayleigh distribution to model noise, and one with a Rician distribut

Answer 1

Yes, you can generate the Rice from chi-squared and Poisson. See any thorough Rice discussion, such as https://en.wikipedia.org/wiki/Rice_distribution:

Another case where Rice(nu,sigma) comes from the following steps:

1. Generate P having a Poisson distribution with parameter (also mean, for a Poisson) lambda = nu^2 / (2*sigma^2).
2. Generate X having a chi-squared distribution with 2P + 2 degrees of freedom.
3. Set R = sigma * sqrt(X).