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December, 1986 Testing Exponentiality Versus a Trend Change in Mean Residual Life
Frank Guess, Myles Hollander, Frank Proschan
Ann. Statist. 14(4): 1388-1398 (December, 1986). DOI: 10.1214/aos/1176350165


Given that an item is of age $t$, the expected value of the random remaining life is called the mean residual life (MRL) at age $t$. We propose two new nonparametric classes of life distributions for modeling aging based on MRL. The first class of life distributions consists of those with "increasing initially, then decreasing mean residual life" (IDMRL). The IDMRL class models aging that is initially beneficial, then adverse. The second class, "decreasing, then increasing mean residual life" (DIMRL), models aging that is initially adverse, then beneficial. We propose two testing procedures for $H_0$: constant MRL (i.e., exponentiality) versus $H_1$: IDMRL, but not constant MRL (or $H'_1$: DIMRL, but not constant MRL). The first testing procedure assumes the turning point, $\tau$, from IMRL to DMRL is specified by the user or is known. The second procedure assumes knowledge of the proportion, $\rho$, of the population that "dies" at or before the turning point (knowledge of $\tau$ itself is not assumed).


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Frank Guess. Myles Hollander. Frank Proschan. "Testing Exponentiality Versus a Trend Change in Mean Residual Life." Ann. Statist. 14 (4) 1388 - 1398, December, 1986.


Published: December, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0613.62122
MathSciNet: MR868307
Digital Object Identifier: 10.1214/aos/1176350165

Primary: 62N05
Secondary: 62G10

Rights: Copyright © 1986 Institute of Mathematical Statistics


Vol.14 • No. 4 • December, 1986
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