General treatment of goodness-of-fit tests based on Kullback–Leibler information

Abstract

This paper introduces a general goodness-of-fit test based on the estimated Kullback–Leibler information. The test uses the Vasicek entropy estimate. Two special cases of the test for location–scale and shape families are discussed. The results are used to introduce goodness-of-fit tests for the uniform, Laplace, Weibull and beta distributions. The critical values and powers for some alternatives are obtained by simulation.

Keywords:

• Kullback–Leibler information
• entropy
• goodness-of-fit tests
• uniform
• Laplace
• Weibull
• beta

Acknowledgements

We thank the associate editor and two referees for giving their valuable comments to improve the quality of the paper.