Computing Maximum Likelihood Parameter Estimates for the Generalized Pareto Distribution with Censored Data

• Main Authors: Wang, Wen-Yen, 王文彥
• Other Authors: Chien-Tai Lin
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/38509412488571315682

碩士 === 淡江大學 === 數學學系 === 86 === The generalized Pareto distribution (GPD) was first introduced by Pickands(1975) to be a stable distribution for excesses over thresholds. This distribution has been the focus of attention in the late 80s and its applications include in the analysis of environmental extreme events,in the study of ozone levels in the upper atmosphere,in the modeling of large insurance claims,and also as an important distribution in reliability studies. Topics associated with this distribution have been extensively considered by numerous researches. Among these are Ahsanullah(1992),Balakrishnan and Ahsanullah(1994), Davison(1984),Grimshaw(1993),Hosking and Wallis(1987),Joe(1987), J. A. Smith(1986),R. L. Smith(1984,1987),Reiss(1989) and others. Employing the approach of Grimshaw(1993),we present a methodology for computing the point and interval maximum likelihood parameter estimation for the two-parameter generalized Pareto distribution with censored data. The main idea underlying our method was given by Davison(1984): A reduction of the two-dimensional numerical search for the zeros of the GPD log-likelihood gradient vector to a one-dimensional numerical search. We describe a computationally efficient algorithm and a computer program (written in C) which implement this approach. Numerical examples for the three censoring cases are illustrated. Also included are results of a simulation study in which the adequacy of the standard error estimates and the practical sample size requirements for the asymptotic normality are evaluated.