Estimating the mean of heavy tailed distribution under random truncation

Abstract

The main aim of this thesis is to deploy and develop a new estimator for the mean that is based on the famous paper by Peng, 2001. Our case focuses on dealing with data when it becomes incomplete with a particular interest in the case of right-truncated, an asymptotic estimator is proposed and its behavior examined in a simulation study. We treat throughout our study two branches: Survival Analysis and Extreme Value Theory which has emerged as one of the most important statistical disciplines for the applied sciences over the last 50 years. The �rst objective of this thesis is to collect and simplify what has been done in the study of extreme values theory. This branch is interested in rare events and the causes of all disasters we know and of all economic crises. In addition, the second objective is to present an introduction that is devoted to the basic notions of survival analysis. Furthermore, we present two cases of incomplete data (censored and truncated) with giving the non-parametric estimator of the mean for each case.