# Random samples from combination of poisson distributions

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RR on 9 Jun 2020
Commented: RR on 11 Jun 2020
How can I generate random samples from a multiple combination of poisson distributions?
I'm wondering if there is the possibility to create a sort of 'poisson' mixture model distribution simular to a gaussian mixture model distribution (gmdistribution function).
RR

Jeff Miller on 9 Jun 2020
One easy way to generate a random score from a poisson mixture distribution is to randomly select the particular poisson first and then randomly select the number from that poisson, something like this:
% generate a random value of x from a poisson mixture distribution:
ru = rand;
if r1<0.2
x = poissrnd(lambda1); % prob = 0.2 that x comes from this distribution
elseif ru<0.5
x = poissrnd(lambda2); % prob = 0.3 that x comes from this distribution
else
x = poissrnd(lambda3); % prob = 0.5 that x comes from this distribution
end
There are various ways to vectorize this for lots of x's, but I'm not sure which would be fastest.
Did you just want the poisson mixture for generating random numbers, or did you want it for some other reason too?

#### 1 Comment

RR on 11 Jun 2020
thank you for the answer. That was the point!
I would like to generate random numbers coming from a combined and weighted poissons distribution to reshape that in a volumetric image (n x m x k matrix).