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New Better than Used and Other Concepts for a Class of Life Distributions
Author(s) -
Rao B. Raja,
Damaraju C. V.,
Rao Pro F. B. Raja,
Damaraju C. V.
Publication year - 1992
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710340805
Subject(s) - class (philosophy) , mathematics , econometrics , statistics , computer science , artificial intelligence
It is well‐known that the inequalities used in the definition of the New Better than Used (N. B. U.) and the New Better than Used in Expectation (N.B.U.E.) concepts, see BARLOW and PROSCHAN (1965, 1975) become equalities if, and only if, the life length of an organism follows an exponential distribution. It is proved in the present paper that these inequalities also reduce to equalities for the class of life distributions that have the “setting the clock back to zero” property. Simple examples of these distributions include the exponential, the linear hazard exponential and the Gompertz distributions. The General Krane distributions (Krane 1963) belong to this class, as well as a recent model introduced by CHIANG and CONFORTI (1989) of a survival distribution in which the hazard rate is a function of the accumulated effect of an individual's continuous exposure to the toxic material in the environment and his biological reaction to the toxin absorbed. As a simple application of the result proved in the paper, the life expectancy of an organism at age γ 0 involved in the N.B.U.E. concept is evaluated for the Gompertzian growth process and for the Chiang and Conforti model.