Characterizations and Infinite Divisibility of Extended COM-Poisson Distribution
Huiming Zhang
TL;DR
This paper characterizes the extended COM-Poisson distribution through various properties and explores conditions under which it is infinitely divisible, linking it to discrete compound Poisson distributions.
Contribution
It introduces new characterizations of the extended COM-Poisson distribution and establishes conditions for its infinite divisibility, connecting it to compound Poisson distributions.
Findings
Characterizations via conditional distribution and Stein identity
Conditions for infinite divisibility of the extended COM-Poisson
Identification of subclasses as discrete compound Poisson distributions
Abstract
This article provides some characterizations of extended COM-Poisson distribution: conditional distribution given the sum, functional operator characterization (Stein identity). We also give some conditions such that the extended COM-Poisson distribution is infinitely divisible, hence some subclass of extended COM-Poisson distributions are discrete compound Poisson distribution.
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Taxonomy
TopicsHolomorphic and Operator Theory · Approximation Theory and Sequence Spaces · Advanced Banach Space Theory