Extended Conway-Maxwell-Poisson distribution and its properties and applications

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

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.

Conway-Maxwell多变量伯努利分布

Conway--Maxwell multivariate Bernoulli distribution

研究Conway-Maxwell多变量伯努利分布家族，展示其参数设定可保持伯努利边缘特性，分析其依赖性质，并证明该家族涵盖所有依赖程度，特定参数范围内满足强Rayleigh性质。

On arbitrarily underdispersed Conway-Maxwell-Poisson distributions

We show that the Conway--Maxwell--Poisson distribution can be arbitrarily underdispersed when parametrized via its mean. More precisely, if the mean $μ$ is an integer then the limiting distribution is a unit probability mass at $μ$. If the mean $μ$ is not an integer then the limiting distribution is a shifted Bernoulli on the two values $\floorμ$ and $\ceilμ$ with probabilities equal to the fractional parts of $μ$. In either case, the limiting distribution is the most underdispersed discrete distribution possible for any given mean. This is currently the only known generalization of the Poisso…

An asymptotic expansion for the normalizing constant of the Conway-Maxwell-Poisson distribution

The Conway-Maxwell-Poisson distribution is a two-parameter generalisation of the Poisson distribution that can be used to model data that is under- or over-dispersed relative to the Poisson distribution. The normalizing constant $Z(λ,ν)$ is given by an infinite series that in general has no closed form, although several papers have derived approximations for this sum. In this work, we start by using probabilistic argument to obtain the leading term in the asymptotic expansion of $Z(λ,ν)$ in the limit $λ\rightarrow\infty$ that holds for all $ν>0$. We then use an integral representation to obtai…

Fractional Poisson random sum and its associated normal variance mixture

In this work, we study the partial sums of independent and identically distributed random variables with the number of terms following a fractional Poisson (FP) distribution. The FP sum contains the Poisson and geometric summations as particular cases. We show that the weak limit of the FP summation, when properly normalized, is a mixture between the normal and Mittag-Leffler distributions, which we call by Normal-Mittag-Leffler (NML) law. A parameter estimation procedure for the NML distribution is developed and the associated asymptotic distribution is derived. Simulations are performed to c…