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Applying the Laplace Transform Procedure, Testing Exponentiality against the NBRU mgf Class

Author

Listed:
  • Naglaa A. Hassan

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

  • Mayar M. Said

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

  • Rasha Abd El-Wahab Attwa

    (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig 44519, Egypt)

  • Taha Radwan

    (Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
    Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said 42526, Egypt)

Abstract

This paper addresses a hypothesis testing problem for comparing exponentially distributed data against a new class termed “New Better than Renewal Used in Moment Generating Function” ( N B R U m g f ). A measure of departure from exponentiality is constructed using the Laplace transform, followed by the development of a U-statistic-based test for the hypothesis. Additionally, a test based on the goodness of fit approach is examined as a special case. The asymptotic normality of the proposed statistic is introduced, and Pitman’s asymptotic efficiency of the two tests is computed and compared with other tests. Percentiles of the test statistics are computed for certain sample sizes in the case of complete data, and the powers of the tests are computed for popular reliability distributions. Finally, practical applications of the proposed tests are demonstrated in multiple cases.

Suggested Citation

  • Naglaa A. Hassan & Mayar M. Said & Rasha Abd El-Wahab Attwa & Taha Radwan, 2024. "Applying the Laplace Transform Procedure, Testing Exponentiality against the NBRU mgf Class," Mathematics, MDPI, vol. 12(13), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2045-:d:1426224
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    References listed on IDEAS

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    1. Everestus O. Ossai & Mbanefo S. Madukaife & Abimibola V. Oladugba, 2022. "A review of tests for exponentiality with Monte Carlo comparisons," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(5), pages 1277-1304, April.
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