Power comparisons of the unbiased Berk-Jones test and the unbiased reversed Berk-Jones test

Abstract

The Berk-Jones test and the reversed Berk-Jones test are shown to be biased by computing the exact minimum power with confidence bands for the continuous distribution function. The bias correction is applied to the Berk-Jones test and the reversed Berk-Jones test by using a similar process of Frey (2009). In order to compose the unbiased test, various critical values are listed. Simulations are used to compare the power of the biased and unbiased Berk-Jones and reversed Berk-Jones tests for various population distributions. Numerical results indicate that the unbiased Berk-Jones test is more powerful than the unbiased reversed Berk-Jones test.

Keywords:

• Bias correction
• Berk-Jones test
• Confidence band
• Reversed Berk-Jones test

Acknowledgments

The author would like to thank the editor and the referee for their valuable comments and suggestions.

Additional information

Funding

The research of the first author was supported by JSPS KAKENHI Grant Number JP18K11199.