A new aging concept derived from the increasing convex ordering |
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| Authors: | T H M Abouelmagd A A E Ahmed Enayat M Abd Elrazik Mahmoud M Mansour A-Hadi N Ahmed |
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| Institution: | 1. Management Information System Department, Taibah University, Saudi Arabia;2. Department of Statistics, Mathematics and Insurance, Benha University, Egypt;3. Department of Statistics, Mathematics and Insurance, Helwan University, Egypt;4. Department of Statistics, Mathematics and Insurance, Benha University, Egypt;5. Management Information System Department, Taibah University, Yanbu, Saudi Arabia;6. Institute of Statistical Studies and Research Cairo University, Egypt |
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| Abstract: | In this paper, a comparison between the life distribution of a new unit with that of a used unit in the increasing convex order is made leading to a new class of life distributions which we call “new better than used in convex ordering of second order”. This class includes as subclasses the NBU and the NBUC and is a subclass of the NBUCA class. Preservation properties under convolution, random maxima, mixing and formation of coherent structures are established. Stochastic comparisons of the excess lifetime when the inter-arrival times belong to the NBUC(2) class are developed. Some applications of Poisson shock models and a test of exponentiality against NBUC(2) alternative are presented. |
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| Keywords: | Classes of life distributions NBU NBUC NBUCA increasing convex order convolution mixing shock models life testing |
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