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. in Mathematics Department, Faculty of Science, Al-Azhar University,

References

: Abdel Aziz, A. A.: On testing exponentiality against RNBRUE alternatives. Appl. Math. Sc. 35, 1725-1736 (2007).

: Abouammoh, A. M.; Abdulghani, S. A.; Qamber, I. S.: On partial orderings and testing of new better than renewal used classes.Reliab.Eng.Syst.Safety.43, 37-41 (1994).

: Abouammoh, A. M.; Ahmed, A. N.: The new better than used class of life distribution. Adv. Appl. Prob. 20, 237-240 (1988).

: Abouammoh, A. M.; Ahmed, A. N.: On renewal failure rate classes of life distributions. Stat. Prob. letters. 14, 211-217 (1992).

: Abouammoh, A. M.; Newby, J. M.: On partial ordering the tests of generalized new better than used class of life distribution. Reliab. Eng. Syst. Safety. 25, 207-217 (1989).

: Abu-Youssef, S. E.: A goodness of fit approach to monotone variance residual life class of life distributions. Appl. Math. Sc. 15, 715-724 (2009).

: Al-Gashgari, F. H.; Shawky, A. I.; Mahmoud, M.A.W.: A nonparametric test for testing exponentiality against NBUCA class of life distributions based on Laplace transform. Qual. Rel. Eng. Int. 32, 29--36 (2016).

: Ahmad, I. A.: A class of statistics useful in testing increasing failure rate average and new better than used life distributions. J. Statist. Plann. Inference. 41, 141-149 (1994).

: Ahmad, I. A.: Moments inequalities of aging families of distributions with hypothesis testing applications. J. Statist. Plann. Inference. 92, 121-132 (2001).

: Ahmad, I.A.; Alwasel, I.A.; Mugdadi, A.R.: A goodness of fit approach to major life testing problems. I. J. Rel. Appl. 2, 81-97 (2001).

: Ahmad, I. A.; Mugdadi, A. R.: Further moments inequalities of life distributions with hypothesis testing applications: the IFRA, NBUC, DMRL classes. J. Statist. Plann. Inference. 120, 1-12 (2004).

: Atallah, M. A.; Mahmoud, M. A. W.; Al- Zahrani, B. M.: A new test for exponentiality versus NBUmgf life distributions based on Laplace transform. Qual. Rel. Eng. Int. 30, 1353--1359 (2014).

: Barlow, R. E.; Proschan, F.: Statistical Theory of Reliability and Life Testing. To Begin with Silver Spring, M D.(1981).

: Bryson, M. C.; Siddiqui, M. M.: Some criteria for ageing. J. Amer. Stat. Assoc. 64, 1472-1483 (1969).

: Deshpande, J. V.; Kochar, S. C.;Singh, H.: Aspects of positive ageing. J. Appl. Prob. 23, 748-758 (1986).

: Grubbs, F. E.: Fiducial bounds on reliability for the two parameter negative exponential distribution. Technometrics. 13, 873-876 (1971).

: Ismail, A. A.; Abu-Youssef, S. E.: A goodness of fit approach to the class of life distribution with unknown age. Qual. Rel. Eng. Int. 25, 761-766 (2012).

: Kango, A. I.: Testing for new is better than used. Comm. Statist. Theory. Methods. 12, 311-321 (1993).

: Kumazawa, Y.: A class of tests statistics for testing whether new is better than used. Comm. Statist. Theory. Methods. 12, 311-321 (1983).

: Lee, A .J.: U-Statistics, Marcel Dekker, New York (1989).

: Mahmoud, M. A. W.; Abdul Alim, N. A.: On testing exponentiality against NBARFR life distributions. Statistica. 4, 619-631 (2002).

: Mahmoud, M. A. W.; Abdul Alim, N. A.: On testing exponentiality against NBURFR class of life distributions. I. J. Rel. Appl. 4, 57-69 (2003).

: Mahmoud, M. A. W.; Abdul Alim, N. A.: A Goodness of fit Approach to for testing NBUFR (NWUFR) and NBAFR (NWAFR) Properties. I. J. Rel. Appl. 9, 125-140 (2008).

: Mahmoud, M. A. W.; EL-arishy, S. M.;Diab, L. S.: Moments inequalities for testing new renewal better than used and renewal new better than used classes. I. J. Rel. Appl. 4, 97-123 (2003).

: Mahmoud, M. A. W.; Diab, L. S.; Kayid, M.: Moments inequalities for NBUL distributions with hypotheses testing applications. Contemp. Engineering Sciences 7, 319-332 (2009).

: Mahmoud, M. A. W.; Moshref, M. E.; Mansour, M. M. M.: A New class of life distributions with hypotheses testing applications. JAPS. 1, 35-47 (2015).

: Mahmoud, M. A. W.; Rady, D. M.: Testing exponentiality against HNBUET class based on goodness of fit approach. Al-Azhar Bull. Sci. 24(1), 81-92 (2013).

: Mahmoud, M. A. W.; EL-Sagheer, R. M.; Etman, W. B. H.: Testing exponentiality aganist new better than renwal used in Laplace transform order. J. Stat. Appl. Pro. 5(2), (2016 to appear)

: Mugdadi, A. R.; Ahmad, I. A.: Moment inequalities derived from comparing life with its equilibrium form. J. Statist. Plann. Inference. 134, 303-317 (2005).

: Shapiro, S. S.: Goodness of Fit Tests in the Exponential Distribution Theory Methods and Applications. Balakrishnan, N.; Basu, A. P. Editors, Gordon and Breach, Amsterdam.(1995).

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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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