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

And

SUBHASH KOCHAR, Indian Statistical Institute, New Delhi

SUMMARY. A life distribution F is called NBUE-NWUE if for some t0 Î (0, ), its mean residual life function e(t) = EF(X - t|X >= t) satisfies e(t) < e(0) for 0<t<t0 for t > t0. 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 p0 = F(t0) is known. Then, assuming that F is either NBUE-NWUE or NWUE-NBUE, we give point estimates and asymptotic confidence intervals for t0 and p0. 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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