Two-Parameter Generalized Pareto Distribution

Abstract

The Pareto distribution has been introduced in Chapter 19. Also discussed in the chapter are a brief review of literature and the methods of estimating its parameters. Kotz and Johnson (1985) provided a detailed discusson of the Pareto distributin. Methods for estimating parameters of the 2-parameter generalized Pareto (GP2) distribution were reviewed by Hosking and Wallis (1987). The method of moments (MOM), maximum likelihood estimation (MLE), and probability weighted moments (PWM) were included in the review. Ashkar and Ouarda (1997) presented some methods of fitting the GP2 distribution using Monte Carlo generated data. They discussed six versions of the generalized method of moments. Wang (1991) derived PWMs for both known and unknown thresholds. van Montfort and Witter (1991) used the MLE method to fit the GP2 distribution to represent the Dutch POT rainfall series, and used an empirical correction formula to reduce bias of the scale and shape parameter estimates. Davison and Smith (1990) used MLE, PWM, and a graphical method to estimate the GP2 distribution parameters. Guo and Singh (1992) and Singh and Guo (1997) employed the principle of maximum entropy (POME) to derive a new method of parameter estimation (Singh and Rajagopal, 1986) for the GP2 distribution. They used Monte Carlo simulated data to evaluate this method and compare it with he MOM, PWM, and MLE methods. The parameter estimates yielded by POME were comparable or better within certain ranges of sample size and coefficient of variation.