計数値の分布として観測された複合正規分布のべータ二項分布による近似に関する研究

概要

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A certain continuous random variable can be often observed as a discrete random variable based on specification limits. In this paper, a compound normally distributed random variable X will be observed as a binary random variable Z based on one-sided specification limit. Beta-binomial approximation of the distribution of X is derived as follows : Firstly, it is analytically examined that the parameter P of the conditional binomial distribution which Z follows distributes approximately with the beta density. Secondly, using the moment method, the distribution of P is approximated to the beta distribution and the degree of approximation is numerically examined. Lastly, it is concluded that the compound normal distribution observed as attributes can be approximated to the beta-binomial distribution.
社団法人日本品質管理学会の論文
1991-10-15