Abstract
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.
