In probability theory and statistics, the Poisson binomial distribution is the discrete probability distribution of a sum of independent Bernoulli trials that are not necessarily identically distributed.

In probability theory, a compound Poisson distribution is the probability distribution of the sum of a number of independent identically-distributed random variables, where the number of terms to be added is itself a Poisson-distributed variable.

In probability theory, the zero-truncated Poisson distribution (ZTP distribution) is a certain discrete probability distribution whose support is the set of positive integers.

A mixed Poisson distribution is a univariate discrete probability distribution in stochastics.