中文摘要：

康威-麦斯威尔-泊松分布是一个有用的离散分布,它是扩展的两参数泊松分布,有关此分布的统计和概率性质被广泛研究和探索;文章以矩母函数为工具讨论了该分布的数字特征和矩,给出了参数点估计的隐式方程和费希尔信息矩阵;最后研究了参数的共轭分布、共轭分布的边际分布和条件分布.

英文摘要：

the Conway-Maxwell-Poisson distribution is a useful discrete distribution, this distribution is a two- parameter extension of the Poisson distribution. Its statistical and probabilistic properties are researched and explored. Taking the moment generating function as a tool, the digital features and moment of the distribution are discussed, the implicit equations about the point estimates of parameters are given, the Fisher information matrix about parameters is derived. Finally we study the conjugate distribution about parameters, the marginal distributions of the conjugate distribution and conditional distributions.