Inference about the transition-point in NBUE-NWUE or NWUE-NBUE Models
Hawkins, D. L.
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A life distribution F is called NBUE-NWUE if for some [see pdf for notation], its mean residual life function[see pdf for notation] satisfies e(t) < e(0) for [see pdf for notation]. If the inequalities for e(t) are reversed on these 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 to unknown. This extends the work of Klefsjo (1989), who devised tests assuming that [see pdf for notation] is known. Then, assuming that F is either NBUE-NWUE or NWUE-NBUE, we give point estimates and asymptotic confidence intervals for to and [see pdf for notation]. The point estimates are asymptotically normal. We rely heavily on the theory of the empirical STTT process discussed in Csorgo, Csorgo and Horvith (1986). Two examples of real-data applications are provided.