How to code a function of the Probability mass function of the Poisson binomial distribution

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Daniel Miller 2016-10-5

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评论： Daniel Miller 2016-10-6

Hello,

I want to use a function that computes the Probability mass function of the Poisson binomial distribution \Pr(K=k)=\sum \limits {{A\in F{k}}}\prod \limits {{i\in A}}p{i}\prod \limits {{j\in A^{c}}}(1-p{j}) https://en.wikipedia.org/wiki/Poisson_binomial_distribution

But how do I implement this sum over subsets of {1,..,n} that contain k elements

Thank you, Daniel

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Answer 1

Peng Liu 2016-10-6

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You may use nchoosek. F_k is nothing but a k-element subset of {1,2,3,...,n}. The sum is over all possible F_k, which can be generated using F_k = nchoosek(1:n,k) (where each row of F_k is a k-element subset)