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A new aging concept derived from the increasing convex ordering
Authors:T. H. M. Abouelmagd  A. A. E. Ahmed  Enayat M. Abd Elrazik  Mahmoud M. Mansour  A-Hadi N. Ahmed
Affiliation: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
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.
Keywords:Classes of life distributions  NBU  NBUC  NBUCA  increasing convex order  convolution  mixing  shock models  life testing
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