Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 265373, 10 pages
http://dx.doi.org/10.1155/2013/265373
Research Article

A Cluster Truncated Pareto Distribution and Its Applications

1Department of Mathematics, Brock University, St. Catharines, ON, Canada L2S 3A1
2Department of Statistics, University of British Columbia, Vancouver, BC, Canada V6T 1Z4
3Department of Mathematics & Statistics, University of Winsdor, Windsor, ON, Canada N9B 3P4

Received 20 June 2013; Accepted 25 July 2013

Academic Editors: E. Omey and S. Sagitov

Copyright © 2013 Mei Ling Huang et al. 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

The Pareto distribution is a heavy-tailed distribution with many applications in the real world. The tail of the distribution is important, but the threshold of the distribution is difficult to determine in some situations. In this paper we consider two real-world examples with heavy-tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and study its properties. We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate the MTPD from a random sample. We apply the MTPD and CTPD to the two examples and compare the proposed method with existing estimation methods. The results of log-log plots and goodness-of-fit tests show that the MTPD and the cluster estimation method produce very good fitting distributions with real-world data.