Strong Convergence Bound of the Pareto Index Estimator under Right Censoring

Abstract

Let {Xn,n≥1} be a sequence of positive independent and identically distributed random variables with common Pareto-type distribution function F(x)=1−x−1/γlF(x) as γ>0, where lF(x) represents a slowly varying function at infinity. In this note we study the strong convergence bound of a kind of right censored Pareto index estimator under second-order regularly varying conditions.