linguistic:voice_change
Poisson-type random measures

The Poisson-type random measures (PT) are a family of three random counting measures which are closed under restriction to a subspace, i.e. closed under Point process operation#Thinning. These random measures are examples of the mixed binomial process and share the distributional self-similarity property of the Poisson random measure. They are the only members of the canonical non-negative power series family of distributions to possess this property and include the Poisson distribution, negative binomial distribution, and binomial distribution. The Poisson random measure is independent on disjoint subspaces, whereas the other PT random measures (negative binomial and binomial) have positive and negative covariances. The PT random measures are discussed and include the Poisson random measure, negative binomial random measure, and binomial random measure.