Poisson-Binomial Distribution
Build success-count probabilities from independent trials with different chances, inspect inclusive events and compare a binomial model with the same mean.
Free theory articleBuild success-count probabilities from independent trials with different chances, inspect inclusive events and compare a binomial model with the same mean.
Concept & interpretation
Four independent components need not have the same chance of working. Counting the working components still produces a finite success-count distribution, but an ordinary binomial model can lose information. The Poisson-binomial distribution keeps every individual chance. Its name does not mean that the count follows a Poisson distribution or a continuous-time Poisson process.