Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 209156, 8 pages
doi:10.1155/2010/209156
Research Article

Strong Convergence Bound of the Pareto Index Estimator under Right Censoring

Bao Tao1 and Zuoxiang Peng2

1College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received 25 October 2009; Revised 14 March 2010; Accepted 11 April 2010

Academic Editor: Siegfried Carl

Copyright © 2010 Bao Tao and Zuoxiang Peng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.