Title

Statistical Analysis Of Old Age Behavior

Keywords

Asymptotic normality; Life distributions; Moment generating function; Moment inequalities; Old age; Pitman efficacy; Remaining life; Stationary variables

Abstract

A random life is characterized by a nonnegative random variable X having survival function (sf) F̄ (x)= P (X > x), x ≥ 0. Associated with any life, two notions are important in life testing. These are the random remaining life at age t, Xt, a random variable with sf F̄t(x) = F̄(x + t)/F̄ (t), x, t ≥ 0, and the corresponding stationary renewal life or the equilibrium life denoted by X̃, whose sf is W̄F (α) = 1/μ ∫x∞ F̄ (u) du, x ≥ 0, where μ = E (X) assumed finite. Thus X̃ may be used to identify "old age." Note that X̃ 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 X̃. We then show that if X̃ is harmonic new is better than used in expectation and if E (X2) 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 X̃ to test that X̃ is exponential against that it belongs to one of several ageing classes. © 2004 Elsevier B.V. All rights reserved.

Publication Date

2-15-2005

Publication Title

Journal of Statistical Planning and Inference

Volume

129

Issue

1-2 SPEC. ISS.

Number of Pages

239-252

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jspi.2004.06.050

Socpus ID

10344232054 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/10344232054

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