On a Mixture Pareto Distribution

• Activity Number: 142
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Mei Ling Huang* and Justyne Mottola and Percy Brill
• Companies: Brock University and Brock University and University of Windsor
• Keywords: Extreme value distributions ; Goodness of fit tests ; Hill estimator ; Finite mixture distribution ; Two-point slope ; Truncated Pareto Distribution

Abstract

The Pareto distribution is a heavy tailed distribution with many applications. In this paper we consider a real world example with heavy tailed observations, which leads us to propose a mixture truncated Pareto distribution (MTPD) and study its properties. There are difficulties in estimating the thresholds of the MTPD. We construct a cluster truncated Pareto distribution (CTPD) by using a two-point slope technique to estimate the MTPD from a random sample. Finally, we apply the MTPD and CTPD to the example which we observed in the beginning, 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 a good fitting distribution with real world data.