Table of Contents
ISRN Probability and Statistics
Volume 2013, Article ID 829131, 12 pages
Research Article

A Weighted Estimation for Risk Model

1Department of Mathematics, Brock University, St. Catharines, ON, Canada L2S 3A1
2Alberta Health, Edmonton, AB, Canada T5J 4R7

Received 16 June 2013; Accepted 19 August 2013

Academic Editors: J. Abellan, P. Dai Pra, and S. Sagitov

Copyright © 2013 Mei Ling Huang and Ke Zhao. 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.


We propose a weighted estimation method for risk models. Two examples of natural disasters are studied: hurricane loss in the USA and forest fire loss in Canada. Risk data is often fitted by a heavy-tailed distribution, for example, a Pareto distribution, which has many applications in economics, actuarial science, survival analysis, networks, and other stochastic models. There is a difficulty in the inference of the Pareto distribution which has infinite moments in the heavy-tailed case. Firstly this paper applies the truncated Pareto distribution to overcome this difficulty. Secondly, we propose a weighted semiparametric method to estimate the truncated Pareto distribution. The idea of the new method is to place less weight on the extreme data values. This paper gives an exact efficiency function, -optimal weights and -optimal weights of the new estimator. Monte Carlo simulation results confirm the theoretical conclusions. The two above mentioned examples are analyzed by using the proposed method. This paper shows that the new estimation method is more efficient by mean square error relative to several existing methods and fits risk data well.