Statistical analysis of old age behavior
Abbreviated Journal Title
J. Stat. Plan. Infer.
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
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 of Statistical Planning and Inference
Article; Proceedings Paper
"Statistical analysis of old age behavior" (2005). Faculty Bibliography 2000s. 4943.