Modifications Based on UMVUEs
5.1 Tests for Poisson, binomial, and negative binomial distributions
Bol’shev and Mirvaliev (1978) were possibly the first to construct the modified chi-squared tests based on Uniformly Minimum Variance Unbiased Estimators (UMVUEs) of the unknown parameters for Poisson, binomial, and negative binomial distributions. The probability mass functions of Poisson, binomial, negative binomial, hypergeometric, and negative hypergeometric distributions are as follows:
Let X be a random variable with its probability ...