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

Naglaa A. Hassan, Mayar M. Said, Rasha Abd El-Wahab Attwa and Taha Radwan ()
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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

Mathematics, 2024, vol. 12, issue 13, 1-14

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.

Keywords: statistical model; nonparametric inference; survival analysis; complete data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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