Estimation of Poisson-Generalized Pareto Compound Extreme Value Distribution by Probability-Weighted Moments and Empirical Analysis

• Published in: Transactions of Tianjin University 2008-02, Vol.14 (1), p.50-54
• Main Author: 刘晶 史道济 吴新荣
• Format: Article
• Language: English
• Subjects: Engineering; Humanities and Social Sciences; Mechanical Engineering; multidisciplinary; Science; 分布特点; 复合矩估算; 数学分析; 最大近似值估算
• ISSN: 1006-4982; 1995-8196
• DOI: 10.1007/s12209-008-0010-1

This paper puts forward a Poisson-generalized Pareto （Poisson-GP） distribution. This new form of compound extreme value distribution expands the existing application of compound extreme value distribution, and can be applied to predicting financial risk, large insurance settlement and high-grade earthquake, etc. Compared with the maximum likelihood estimation （MLE） and compound moment estimation （CME）, probability-weighted moment estimation （PWME） is used to estimate the parameters of the distribution function. The specific formulas are presented. Through Monte Carlo simulation with sample sizes 10, 20, 50, 100, 1 000, it is concluded that PWME is an efficient method and it behaves steadily. The mean square errors （MSE） of estimators by PWME are much smaller than those of estimators by CME, and there is no significant difference between PWME and MLE. Finally, an example of foreign exchange rate is given. For Dollar/Pound exchange rates from 1990-01-02 to 2006-12-29, this paper formulates the distribution function of the largest loss among the investment losses exceeding a certain threshold by Poisson-GP compound extreme value distribution, and obtains predictive values at different confidence levels.