广义几何分布、Harris分布、负二项分布和Γ分布的特征
Characterizations of the Extended Geometric, Harris, Negative Binomial and Gamma Distributions
摘要：
定义了广义几何分布，并利用具有完全单调概率序列的性质刻画了其混合分布。此外，卷积方程和概率母函数被用来表征扩展的几何分布。进一步，基于概率母函数给出了Harris分布和负二项分布的一些特征.导出了这些分布之间的关系，最后用拉普拉斯变换刻画了一个Γ分布。
英文摘要：
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize extended geometric distributions. Further, some characterizations of Harris and negative binomial distributions based on probability generating functions are obtained. Relations between these distributions are derived and finally a gamma distribution is characterized in terms of its Laplace transform.
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。
