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A test of exponentiality against ℳ alternatives

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  • Priyanka Majumder
  • Murari Mitra

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.

Suggested Citation

  • Priyanka Majumder & Murari Mitra, 2019. "A test of exponentiality against ℳ alternatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(3), pages 794-812, July.
    • Handle: RePEc:taf:gnstxx:v:31:y:2019:i:3:p:794-812
    DOI: 10.1080/10485252.2019.1643464
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    Cited by:

    1. Walid B. H. Etman & Mohamed S. Eliwa & Hana N. Alqifari & Mahmoud El-Morshedy & Laila A. Al-Essa & Rashad M. EL-Sagheer, 2023. "The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data," Mathematics, MDPI, vol. 11(13), pages 1-22, June.

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