Moments Inequalities for NBRUL Distributions with Hypotheses Testing Applications

Authors

  • Rashad Mohamed El-Sagheer Mathematics Department, Faculty of Science, Al-Azhar University
  • Mohamed A. W. Mahmoud Mathematics Department, Faculty of Science, AL-Azhar University, Nasr City 11884, Cairo, Egypt
  • Walid B. H. Etman Mathematics Department, Faculty of Science, AL-Azhar University, Nasr City 11884, Cairo, Egypt

DOI:

https://doi.org/10.17713/ajs.v47i1.579

Abstract

In this paper, moment inequalities for the new better than renwal used in Laplace transform order ( NBRUL ) class of ageing distributions are derived. This inequalities demonstrate that if the mean life is finite, then all higher order moments exist. A new test for exponentiality versus NBRUL can be constructed using thes inequalities. Pitman's asymptotic efficiencies and critical values of the proposed test are calculated and tabulated. The powers of this test are estimated for some famously alternatives distributions in reliability such as Linear failure rate,Weibull and gamma distributions. Finally, examples in different areas are used as a practical applications of the proposed test.

Author Biography

Rashad Mohamed El-Sagheer, Mathematics Department, Faculty of Science, Al-Azhar University

Prof. inĀ Mathematics Department, Faculty of Science, Al-Azhar University,

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Published

2018-01-30

How to Cite

El-Sagheer, R. M., Mahmoud, M. A. W., & Etman, W. B. H. (2018). Moments Inequalities for NBRUL Distributions with Hypotheses Testing Applications. Austrian Journal of Statistics, 47(1), 95-104. https://doi.org/10.17713/ajs.v47i1.579

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Articles