ON ESTIMATING CHANGE POINT IN A MEAN RESIDUAL LIFE FUNCTION

Let F be the cumulative distribution function (c.d.f.) of a non-negative random variable with the probability density function (p.d.f.) f and the mean residual life (m.r.l.) function m(t). It is assumed that m(t) is truncated "up side down bath-tub" model, that is, m(t) is non-decreasing continuous function for t < tau and is constant t greater-than-or-equal-to tau. In this paper a procedure for estimating tau is proposed assuming that there exist a known p(o) with 0 < F(tau) < p(o) < 1. The estimator is shown to be consistent and the asymptotic distribution is given. Also considered a specific parametric model, with I(A) denoting the indicator function of A, m(t) = (mu+ct) I(0 less-than-or-equal-to t < tau)+(mu+c-tau)I(t greater-than-or-equal-to tau). Two estimates for tau have been proposed and their proposed have been proved. Some simulations comparing the performance of these estimates are carried out and an example is given.