## Annals of Statistics

### Testing Exponentiality Versus a Trend Change in Mean Residual Life

#### Abstract

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).

#### Article information

Source
Ann. Statist., Volume 14, Number 4 (1986), 1388-1398.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350165

Digital Object Identifier
doi:10.1214/aos/1176350165

Mathematical Reviews number (MathSciNet)
MR868307

Zentralblatt MATH identifier
0613.62122

JSTOR
links.jstor.org

Subjects
Primary: 62N05: Reliability and life testing [See also 90B25]
Secondary: 62G10: Hypothesis testing

#### Citation

Guess, Frank; Hollander, Myles; Proschan, Frank. Testing Exponentiality Versus a Trend Change in Mean Residual Life. Ann. Statist. 14 (1986), no. 4, 1388--1398. doi:10.1214/aos/1176350165. https://projecteuclid.org/euclid.aos/1176350165