Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series A, Pt. 1, 117-132

INFERNCE ABOUT THE TRANSITION-POINT IN NBUE-NWUE MODELS

By

D. L. HAWKINS, *University of Texas, Arlington*

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*And

SUBHASH KOCHAR, *Indian Statistical Institute, New Delhi*

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SUMMARY. A life distribution *F* is called NBUE-NWUE if for some *t*_{0} Î (0, ¥), its mean residual life function e(*t*) = *E*_{F}(*X* - *t*|*X* >= *t*) satisfies e(*t*) < e(0) for 0<*t*<*t*_{0} for *t* > *t*_{0}. If the inequalities for e(*t*) are reversed on those time intervals, it is called NWUE-NBUE. Using a characterization of such distributions in terms of the scaled total-time-on-test transform (STTT), we first give tests of exponentiality versus NBUE-NWUE or NWUE-NBUE with t0 unknown. This extends the work of Klefsjo (1989), who devised tests assuming that *p*_{0} = *F(t*_{0}) is known. Then, assuming that *F* is either NBUE-NWUE or NWUE-NBUE, we give point estimates and asymptotic confidence intervals for *t*_{0} and *p*_{0}. The point estimates are asymptotically normal. We rely heavily on the theory of the empirical STTT process discussed in Csorgo,Csorgo and Horvath (1986).

*AMS (1991) subject classification.* 62N05, 62G05

*Key words and phrases*. Weak convergence, nonparametric inference, reliability, NBUE, NWUE, total time on test transform, Brownian bridge process, hypothesis testing, interval estimation.

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