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Estimation of poisson-generalized pareto compound extreme value distribution by probability-weighted moments and empirical analysis

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Abstract

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.

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Authors and Affiliations

  1. School of Management, Tianjin University, Tianjin, 300072, China

    Jing Liu

  2. School of Sciences, Tianjin University, Tianjin, 300072, China

    Daoji Shi & Xinrong Wu

Authors
  1. Jing Liu
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  2. Daoji Shi
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  3. Xinrong Wu
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Corresponding author

Correspondence to Jing Liu.

Additional information

Supported by National Natural Science Foundation of China (No. 70573077).

LIU Jing, born in 1979, female, doctorate student.

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Liu, J., Shi, D. & Wu, X. Estimation of poisson-generalized pareto compound extreme value distribution by probability-weighted moments and empirical analysis. Trans. Tianjin Univ. 14, 50–54 (2008). https://doi.org/10.1007/s12209-008-0010-1

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  • DOI: https://doi.org/10.1007/s12209-008-0010-1

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