A Family of Bivariate Distributions Generated by the Bivariate Bernoulli Distribution
从二元伯努利分布出发，将一维的二项、负二项、泊松、伽马和正态分布推广到二维，得到并研究了一族二元分布。
Abstract If X 1, X 2, … is a sequence of independent Bernoulli random variables, the number of successes in the first n trials has a binomial distribution and the number of failures before the rth success has a negative binomial distribution. From both the binomial and the negative binomial distributions, the Poisson distribution is obtainable as a limit. Moreover, gamma distributions (integer shape parameters) are limits of negative binomial distributions, and the normal distribution is a limit of negative binomial, Poisson, and gamma distributions. These basic facts from elementary probability have natural extensions to two dimensions because there is a unique natural bivariate Bernoulli distribution. In this article, such extensions yielding a family of bivariate distributions are obtained and studied.