Statistical analysis of old age behavior

    Authors

    I. A. Ahmad

    Comments

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    Abbreviated Journal Title

    J. Stat. Plan. Infer.

    Keywords

    life distributions; remaining life; old age; stationary variables; moment generating function; moment inequalities; asymptotric normality; Pitman efficacy; LIFE DISTRIBUTIONS; MOMENTS INEQUALITIES; TESTING APPLICATIONS; NBUC; Statistics & Probability

    Abstract

    A random life is characterized by a nonnegative random variable X having survival function (sf) F(x) = P (X > x), x greater than or equal to 0. Associated with any life, two notions are important in life testing. These are the random remaining life at age t, X-t, a random variable with sf F-t (x) = F(x + t)/F (t), x, t greater than or equal to 0, and the corresponding stationary renewal life or the equilibrium life denoted by X, whose sf is W-F(alpha) = 1/mu integral(x)(infinity) F(u) du, x greater than or equal to 0, where mu = E(X) assumed finite. Thus may be used to identify "old age." Note that, is unobservable but can be studied through X itself. In the current investigation, inequalities of the moments of X are derived from the ageing behavior of X. We then show that if is harmonic new is better than used in expectation and if E (X-2) exists, then the moment generating function of X exists and its upper bound is obtained. We also use moments inequalities derived from the ageing behavior of : to test that is exponential against that it belongs to one of several ageing classes. (C) 2004 Elsevier B.V. All rights reserved.

    Journal Title

    Journal of Statistical Planning and Inference

    Volume

    129

    Issue/Number

    1-2

    Publication Date

    1-1-2005

    Document Type

    Article; Proceedings Paper

    Language

    English

    First Page

    239

    Last Page

    252

    WOS Identifier

    WOS:000226222300016

    ISSN

    0378-3758

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