Abstract

Let X and Y be two random variables denoting life times having finite means. Let, S 1 , S 2 and M 1 , M 2 denote their survival and MRL functions, respectively. X is said to be smaller than Y in mean residual life order, if and only if [Special characters omitted.] In this thesis smooth estimators for the survival and MRL functions under the above ordering are studied. Nonparametric method given by Hu et al. (2002) has shown good properties, but it is not smooth enough, when the true function is continuous. Chaubey and Sen (1996) have proposed a new approach to smooth survival and density function in stead of the popular kernel method. Following their approach, we introduce two methods for smooth estimation of a survival function based on the two criteria of mean residual life ordering. The strong uniform consistency of the estimators has also been shown here. Numerical studies based on simulation indicate both smooth estimators to be superior to the estimator due to Hu et al. (2002) in terms of bias and MSE in majority of cases.