Browse > Article

On NBUmgf class at specific age  

Gadallah, A.M. (Department of Basic Sciences, Thebes Higher Institute for Engineering Thebes Academy)
Publication Information
International Journal of Reliability and Applications / v.17, no.2, 2016 , pp. 107-119 More about this Journal
Abstract
A new concept of aging classes namely new better (worse) than used at age $t_0$ in moment generating function order, $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$) is introduced. For the classes $NBU_{mgf}-t_0$ ($NWU_{mgf}-t_0$), preservation under convolution, mixture, mixing and the homogeneous Poisson shock model are studied. In the sequel, nonparametric test is proposed, the asymptotic normality of the class is established and the asymptotic null variance is estimated. The percentiles and powers of this test are tabulated. The asymptotic efficiencies for some alternatives distributions are derived. Finally sets of real data are used as examples to elucidate the use of the proposed test in practical application.
Keywords
convolution; hypothesis test; mixture; Poisson shock model; U-Statistic;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Ahmad, I. A.and Kayid, M. (2004). Some results about $NBU_{mgf}$ class of life distribution, International Journal of Reliability and Applications, 5, 155-162.
2 Attia, A. F., Mahmoud, M. A. W. and Tiab, I. B. (2005). On testing exponential better than used in average based on the total time on test transform, The 7th Annual Conference on Statistics and Modeling in Human and Social Science, 76-83.
3 Barlow, R. E. and proschan, F. (1981). Statistical Theory of Reliability and Life Testing Probability Models, To begin with, Silver Spring, MD.
4 Bryson, M. C. and Siddiqui, M. M. (1969). Some criteria for aging, Journal of the American Statistical Association, 64, 1472-1483.   DOI
5 Deshpande, J. V., Kochar, S. C. and Singh, H. (1986). Aspects of positive aging, Journal of Applied Probability, 288, 773-779.
6 Ebrahimi, N. and Habbibullah, M. (1990). Testing whether the survival distribution is new better than used of specified age, Biometrika, 77, 212-215.   DOI
7 Edgman R. L., Scott R. C. and Pavur R. J. (1988). A modified kolmogorov- smirnov test for the inverse Gaussian density with unknown parameters, Communications in Statistics-simulation and Computations, 17, 1203-1212.   DOI
8 Esary, J. D., Marshal, A. W. and Proschan, F. (1969). Shock models and wear process, Annals of Probability, 1, 627-649.
9 Hollander, R. M., Park, D. H. and Proschan, F. (1986). A class of life distributions for aging, Journal of the American Statistical Association, 81, 91-95.   DOI
10 Hollander, R. M. and Proschan, F. (1972). Testing whether new is better than used, Annals of Mathematical Statistics, 43, 1136-1146.   DOI
11 Klefsjo, B. (1981). HNBUE survival under some shock models, Scandinavian Journal of Statistics, 8, 39-47.
12 Li, X. (2004). Some properties of aging notions based upon the moment generating function order, Journal of Applied Probability, 41, 927-934.   DOI
13 Mahmoud, M. A. W. and Gadallah, A. M. (2012). Moment inequalites of NBUmgf with testing hypotheses application, International Journal of Reliability and Applications, 13, 57-69.
14 Mahmoud, M. A. W., Moshref, M. E., Gadallah, A. M. and Shawky, A. I. (2013). New classes at specific age: properties and testing hypotheses, Journal of Statistical Theory and Applications, 12, 106-119.   DOI
15 Mahmoud, M. A. W., Moshref, M. E. and Gadallah, A. M. (2014). On NBUL class at specific age, International Journal of Reliability and Applications, 15, 11-22.
16 Muller, A. and Stoyan D. (2002). Coparison Methods for Queues and Other Stochastic Models, Wiley & sons, New York.
17 Zhang, S. and Li, X. (2004). Preservation property of $NBU_{mgf}$ under shock models, International Journal of Reliability and Applications, 4, 71-77.
18 Parameshwar, V. Pandit and Anuradha, M. P. (2007). On testing exponentiality against new better than used of specified age, Statistical Methodology, 4, 13-21.   DOI
19 Shaked, M. and Shanthikumar, J.G. (1994). Stochastic Orders and their Applications, Academic press, New York.
20 Wang, W. Y. (1996). Life distribution classes and two unit standby redundant system, Ph.D. dissertation, Chinese Academy of Science, Beijing.
21 Lawless, J. F. (1982). Statistical Models & Methods for Lifetime Data, Wiley & sons, New York.
22 Ahmad, I. A. (1998). Testing whether a survival distribution is new better than used of an unknown specified age, Biometrka, 85, 451-456.   DOI