Abstract

A bivariate generalized Yule distribution is introduced here as the distribution of the random sum of certain types of independent and identically distributed bivariate Bernoulli random variables. We study some important properties of the distribution through deriving explicit expressions for its probability mass function, factorial moments, and the probability generating function (p.g.f.) of its conditional distributions. Certain recurrence relations for its probabilities, raw moments and factorial moments are also developed. The method of maximum likelihood is employed for estimating the parameters of the distribution and applied to real life data sets for illustrating the relevance of the distribution.

摘要

这里引入二元广义尤尔分布作为某些类型的独立且同分布的二元伯努利随机变量的随机和的分布。我们通过推导其概率质量函数、阶乘矩及其条件分布的概率生成函数 (pgf) 的显式表达式来研究分布的一些重要属性。还开发了其概率、原始矩和阶乘矩的某些递推关系。采用最大似然法来估计分布的参数，并将其应用于现实生活数据集以说明分布的相关性。