Integral form of the COM-Poisson normalization constant

TL;DR

This paper introduces an integral expression for the COM-Poisson normalization constant, providing a potentially useful analytical tool for understanding and computing this function in statistical modeling.

Contribution

The paper presents the first integral form of the COM-Poisson normalization constant, expanding analytical options for this distribution.

Findings

Provides an integral expression for Z(λ, ν) on the real axis

Enables new analytical and computational approaches

Facilitates further theoretical analysis of COM-Poisson distribution

Abstract

In this brief note an integral expression is presented for the COM-Poisson renormalization constant $Z(\lambda, \nu)$ on the real axis.