enter image description here

The Poisson Binomial Distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed. The first four moments of this distribution are shown in the figure (source: https://en.wikipedia.org/wiki/Poisson_binomial_distribution).

Suppose we are not dealing with a series of typical Bernoulli trials. Rather, suppose we are dealing with trials, where each Bernoulli Distribution $i$ is multiplied by constant, $c_i$, such that some trials are essential weighted more than others.

What are the moments of this more general Poisson Binomial Distribution?


A Poisson binomial distribution is a sum of $n $ independent Bernoulli distributed variables, so that by definition their moments are the sums of the moments of the $n$ Bernoulli distributions. For any value of $i $ (i.e., for any of these Bernoulli distributed variables), if $p_i $ is multiplied by a constant $c_i $, the resulting moments are simply obtained by substituting $p_i $ with $p_i \cdot c_i $. Extending this to the sums over all $n $ possible values of $i $ you can get the moments for this generalized Poisson binomial distribution.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.