A modified Conway-Maxwell-Poisson type binomial distribution and its applications

TL;DR

This paper introduces a new four-parameter generalized binomial distribution derived from queueing systems and Conway-Maxwell-Poisson variables, exploring its properties, estimation methods, and applications.

Contribution

It presents a novel four-parameter distribution based on queueing theory and CMP variables, with detailed properties and practical estimation techniques.

Findings

Derived from queueing systems with state-dependent rates

Analyzed properties like dispersion, skewness, kurtosis

Demonstrated applications and estimation methods

Abstract

This paper proposes a generalized binomial distribution with four parameters, which is derived from the finite capacity queueing system with state-dependent service and arrival rates. This distribution is also generated from the conditional Conway-Maxwell-Poisson distribution given a sum of two Conway-Maxwell-Poisson variables. In this paper, we consider the properties about the probability mass function, index of dispersion, skewness and kurtosis and give applications of the proposed distribution from its geneses. The estimation method and simulation study are also considered.