Estimating the probability of obtaining nonfeasible parameter estimates of the generalized pareto distribution

In this paper we consider the problem of estimating the parameters of the Generalized Extreme-Value distribution. The popular method of probability-weighted moments does not guarantee that estimates will be consistent with the observed data. We present a simple program to predict the probability of obtaining such nonfeasible estimates. Our estimation techniques are based on results from intensive simulations and the successful modelling of the lower tail of the distribution of the upper bound of the support. More simulations are performed to validate the new procedure.

[1]  Malcolm R Leadbetter,et al.  On a basis for 'Peaks over Threshold' modeling , 1991 .

[2]  J. V. Witter,et al.  Testing exponentiality against generalised Pareto distribution , 1985 .

[3]  J. Pickands.  Statistical Inference Using Extreme Order Statistics , 1975 .

[4]  Richard L. Smith.  Threshold Methods for Sample Extremes , 1984 .

[5]  Richard L. Smith.  Estimating tails of probability distributions , 1987 .

[6]  J. R. Wallis,et al.  Probability weighted moments compared with some traditional techniques in estimating Gumbel Parameters and quantiles , 1979 .

[7]  William H. Press,et al.  Numerical Recipes: FORTRAN , 1988 .

[8]  J. R. Wallis,et al.  Estimation of the generalized extreme-value distribution by the method of probability-weighted moments , 1985 .

[9]  J. R. Wallis,et al.  Probability Weighted Moments: Definition and Relation to Parameters of Several Distributions Expressable in Inverse Form , 1979 .

[10]  A. Jenkinson.  The frequency distribution of the annual maximum (or minimum) values of meteorological elements , 1955 .

[11]  R. Fisher,et al.  Limiting forms of the frequency distribution of the largest or smallest member of a sample , 1928, Mathematical Proceedings of the Cambridge Philosophical Society.

[12]  J. Hosking,et al.  Parameter and quantile estimation for the generalized pareto distribution , 1987 .

[13]  Anthony C. Davison,et al.  Modelling Excesses over High Thresholds, with an Application , 1984 .

[14]  M. Falk.  A note on generalized Pareto distributions and thek upper extremes , 1990 .