An efficient correction to the density-based empirical likelihood ratio goodness-of-fit test for the inverse Gaussian distribution

ABSTRACT

The inverse Gaussian (IG) distribution is widely used to model positively skewed data. An important issue is to develop a powerful goodness-of-fit test for the IG distribution. We propose and examine novel test statistics for testing the IG goodness of fit based on the density-based empirical likelihood (EL) ratio concept. To construct the test statistics, we use a new approach that employs a method of the minimization of the discrimination information loss estimator to minimize Kullback–Leibler type information. The proposed tests are shown to be consistent against wide classes of alternatives. We show that the density-based EL ratio tests are more powerful than the corresponding classical goodness-of-fit tests. The practical efficiency of the tests is illustrated by using real data examples.

KEYWORDS:

• Empirical likelihood ratio
• goodness-of-fit tests
• inverse Gaussian distribution
• Kullback–Leibler information
• minimum discrimination information loss estimator

Acknowledgements

The authors are grateful to three anonymous referees and the associate editor for providing some useful comments on an earlier version of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.