O'Reilly logo

Chi-Squared Goodness of Fit Tests with Applications by M.S Nikulin, Vassilly Voinov, N. Balakrishnan

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

Chapter 5

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:

imageimage

Let X be a random variable with its probability ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required