A test of exponentiality against ℳ alternatives

ABSTRACT

This paper introduces a test for detecting moment generating function order dominance. We develop a family of scale-invariant test statistics based on the weighted integrals of the difference between the empirical moment generating function and the mgf of an appropriate exponential distribution. The asymptotic distributions of our test statistics are derived and consistency of the test is established. We compute the local approximate Bahadur efficiency of the test against certain typical alternatives. The performance of the test is assessed by means of a simulation study. A suitable modification of the test under random censorship is also studied. Finally, we apply the test to some well-known real-life data sets for illustration in both the scenarios.

KEYWORDS:

• Moment generating function order
• $\mathcal{M}$-class
• asymptotic normality
• local approximate Bahadur efficiency
• random censorship

Disclosure statement

No potential conflict of interest was reported by the authors.