Parameter and quantile estimation for the generalized pareto distribution

The generalized Pareto distribution is a two-parameter distribution that contains uniform, exponential, and Pareto distributions as special cases. It has applications in a number of fields, including reliability studies and the analysis of environmental extreme events. Maximum likelihood estimation of the generalized Pareto distribution has previously been considered in the literature, but we show, using computer simulation, that, unless the sample size is 500 or more, estimators derived by the method of moments or the method of probability-weighted moments are more reliable. We also use computer simulation to assess the accuracy of confidence intervals for the parameters and quantiles of the generalized Pareto distribution.

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

[2]  N. L. Johnson,et al.  Linear Statistical Inference and Its Applications , 1966 .

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

[4]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[5]  O. Kempthorne,et al.  Maximum Likelihood Estimation in the Three‐Parameter Lognormal Distribution , 1976 .

[6]  B. Efron,et al.  Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher information , 1978 .

[7]  J. R. Wallis,et al.  Estimation of parameters and quantiles of Wakeby Distributions: 1. Known lower bounds , 1979 .

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

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

[10]  P. Prescott,et al.  Maximum likeiihood estimation of the parameters of the three-parameter generalized extreme-value distribution from censored samples , 1983 .

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

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

[13]  Richard L. Smith.  Maximum likelihood estimation in a class of nonregular cases , 1985 .

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

[15]  J. Hosking.  Maximum‐Likelihood Estimation of the Parameters of the Generalized Extreme‐Value Distribution , 1985 .

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