一种新的过离散计数模型
A new over-dispersed count model
AI总结：
本研究提出由泊松与几何随机变量卷积得到的PoiG双参数离散分布，推导其统计性质与参数估计方法，可更有效地用于过离散及等离散计数数据建模。
摘要：
本文通过泊松随机变量与独立分布的几何随机变量的卷积，推导得到一种新的双参数离散分布，即PoiG分布。该分布是泊松分布与几何分布的推广，可用于对过离散及等离散计数数据建模。本文研究了该计数模型的多项重要统计性质，包括概率生成函数、矩生成函数、各阶矩、生存函数与风险率函数；还详细探究了对数凹性、随机序等单调性性质。文中给出了该模型参数的矩估计与极大似然估计方法。预计相较于同类竞争模型，该分布对从业者处理过离散计数数据建模问题更具实用价值。
英文摘要：
A new two-parameter discrete distribution, namely the PoiG distribution is derived by the convolution of a Poisson variate and an independently distributed geometric random variable. This distribution generalizes both the Poisson and geometric distributions and can be used for modelling over-dispersed as well as equi-dispersed count data. A number of important statistical properties of the proposed count model, such as the probability generating function, the moment generating function, the moments, the survival function and the hazard rate function. Monotonic properties are studied, such as the log concavity and the stochastic ordering are also investigated in detail. Method of moment and the maximum likelihood estimators of the parameters of the proposed model are presented. It is envisaged that the proposed distribution may prove to be useful for the practitioners for modelling over-dispersed count data compared to its closest competitors.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
