In this thesis, we present an expanded account of mean residual life estimation based on an article by Belkacem Abdous, Alexandre Berred (2005). The mean residual life function is of interest in many fields such as reliability, survival analysis, actuarial studies, medicine research life actuary studies, social science and some others statistical research. Consider a unite with age t, which means that it is working since time of t and can continue working after t. Residual life of this unit after time of t, is random variable and the expectation of this lifetime random variable is called mean residual life in time of t. Because of the important of this conception and its many application, and on the other hand, distribution of populations being unknown, its estimation is essential. In this paper , the purpose is to estimate mean residual life, by means of nonparametric estimation methods in two cases of complete data and censored data. Given a sample from an unknown distribution, we use the local linear fitting technique to estimated the corresponding mean residual life function. The limit of behaviour of the obtained estimator is presented. There has been a lot of work available on the inference of MRL in the complete data setting. Howere, the observations for X are often censored. Inference for MRL becomes more involved under random censorship. In this paper, an empirical likelihood procedure is proposed for the inferenceof MRL with right censored data. It is shown that the limiting distribution of the empirical log-likelihood ratio for MRL is a scaled chi-square distribution. The limiting distribution can be used to construct empirical likelihood based confidence intervals for MRL. Numeric result from a simulation study suggest that the empirical likelihood based confidence intervals have better coverage than the existing normal approximation based confidence intervals. In this way, biased asymptotical behaviour and the variance of outcome estimate is analysis finally simulation results are studied.