On Testing Exponentiality against NBAFR Alternatives

Abstract

In this article, we propose an interesting approach for testing exponentiality against NBAFR alternatives. A measure of deviation from exponentiality has been derived on the basis of an inequality which we have proved. A test statistic has been constructed using density estimators and its asymptotic normality established. The consistency of the said test is also proved.

Keywords:

• NBAFR
• Density estimation
• Asymptotic normality

Mathematics Subject Classification:

• Primary 62G10
• Secondary 62N05
• 90B25
• 62G07

Acknowledgments

We are grateful to the Associate Editor and the referees for their careful reading of an earlier version of this article and their constructive suggestions which led to substantial improvement in the presentation. The third author is grateful to his student Mr. Kinjal Basu for his help with the simulations.