MATLAB: Compound Poisson Distribution Model

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Hey Everyone,
I have the probability density function of a Negative-binomial Distribution (Compound Poisson Distribution) and I would like to generate random numbers based on probability similar to how binornd function works. The following is the compound model written in matlab:
fun = @(lambda) (lambda.^k).*(exp(-1.*lambda)).* gampdf(lambda,alpha,beta)./factorial(k);
P(k)= integral(fun,0,Inf);
I assume the number of trials (k) from 0:7 and the output is the probability of each point P(k). So now I only need to choose random numbers from this distribution based on their probability values.
Thanks in advance.

Best Answer

I am not sure if I understand your question correctly. I guess once you get P, then you would like to choose its elements randomly, right? If so, you can use the following code:
alpha = 1; beta = 1; % replace by your desired values
for k = 0:7
    fun = @(lambda) (lambda.^k).*(exp(-1.*lambda)).* gampdf(lambda,alpha,beta)./factorial(k);
    P(k+1) = integral(fun,0,Inf);
end
out = datasample(P,1) % 1 observation, replace 1 by higher value for more observations
This will be uniformly random. If you are interested then you may use:
out = P(randperm(numel(P),1))
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