International Journal of Reliability and Applications

The Korean Reliability Society (한국신뢰성학회)
권호 표지

A new test of exponentiality against NDVRL

  • Hassan, M.KH. (Department of Mathematics, Faculty of Education, Ain Shams University)
  • Received : 2015.05.23
  • Accepted : 2015.11.03
  • Published : 2015.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, the problem of testing exponentiality against net decreasing variance residual lifetime (NDVRL) classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's asymptotic relative efficiency (PARE) is discussed to assess the performance of the test with respect to other tests. Selected critical values are tabulated. Some numerical simulations on the power estimates are presented for proposed test. Finally, numerical examples are presented for the purpose of illustrating our test.

Keywords

References

  1. Abu-Youssef, S. E. (2007). Testing decreasing (increasing) variance residual life class of life distributions using kernel method, Applied Mathematical Sciences, 1, 1915-1927.
  2. Abu-Youssef, S. E. (2009). A Goodness of fit approach to monotone variance residual life class of life distributions, Applied Mathematical Sciences, 3, 715-724.
  3. Ahmad, I. A. (1992). A new test for mean residual life time, Biometrika, 79, 416-419. https://doi.org/10.1093/biomet/79.2.416
  4. Ahmad, I. A. (2001). Moments inequalities of ageing families of distributions with hypothesis testing application, Journal of Statistical Planning and Inference, 92, 121-132. https://doi.org/10.1016/S0378-3758(00)00139-7
  5. Attia, A. F., Mahmoud, M. A. W. and Abdul-Moniem, I. B. (2004). On testing for exponential better than used in average class of life distributions based on the U-test, The proceeding of the 39th annual conference on statistics, SR Cairo university-Egypt, 11-14.
  6. Al-Zahrani, B. and Stoyanov, J. (2008). Moment inequalities for DVRL distributions, characterization and testing for exponentiality, Journal Statistics and Probability Letters, 78, 1792-1799. https://doi.org/10.1016/j.spl.2008.01.045
  7. Al-Zahrani, B. (2012). Nonparametric testing for exponentiality versus net decreasing variance residual lifetime, Journal of Quality Technology of Quantitative Management, 9, 435-442. https://doi.org/10.1080/16843703.2012.11673303
  8. Gupta, C. (2006). Variance residual life function in reliability studies, METRON - International Journal of Statistics, 3, 343-355.
  9. Hollander, M. and Prochan, F. (1972). Testing whether new is better than used, The Annals of Mathematical Statistics, 43, 1136-1146. https://doi.org/10.1214/aoms/1177692466
  10. Kanwar, S. and Madhu, B. J. (1991). A test for the variance residual life, Communications in Statistics: Theory and Methods, 20, 327-331. https://doi.org/10.1080/03610929108830500
  11. Kaplan, E.L. and Meier, P. (1958). Nonparameteric estimation from incomplete observations, Journal of American Statistical Association, 53, 457-481. https://doi.org/10.1080/01621459.1958.10501452
  12. Marshall, A. W. and Proschan, F. (1972). Classes of life distributions applicable in replacement with renewal theory implications, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, 1, 395-415.
  13. Sen, K. and Jain, M. B. (1991). A test for the variance residual life, Communications in Statistics, 20, 327-331. https://doi.org/10.1080/03610929108830500
  14. Serfling, R. J.(1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.