论文信息 - Goodness-of-Fit Tests for the Generalized Pareto Distribution

Goodness-of-Fit Tests for the Generalized Pareto Distribution

Tests of fit are given for the generalized Pareto distribution (GPD) based on Cramér–von Mises statistics. Examples are given to illustrate the estimation techniques and the goodness-of-fit procedures. The tests are applied to the exceedances over given thresholds for 238 river flows in Canada; in general, the GPD provides an adequate fit. The tests are useful in deciding the threshold in such applications; this method is investigated and also the closeness of the GPD to some other distributions that might be used for long-tailed data.

Vartan Choulakian | Michael A. Stephens | M. Stephens | V. Choulakian

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

[2] D. Darling,et al. The Cramer-Smirnov Test in the Parametric Case , 1955 .

[3] John J. Spinelli,et al. Cramér‐von Mises tests of fit for the Poisson distribution , 1997 .

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

[5] Debbie J. Dupuis,et al. Estimating the probability of obtaining nonfeasible parameter estimates of the generalized pareto distribution , 1996 .

[6] S. Grimshaw. Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution , 1993 .

[7] Michael A. Stephens,et al. Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters , 1976 .

[8] A. Hadi,et al. Fitting the Generalized Pareto Distribution to Data , 1997 .

[9] Min Tsao,et al. A hybrid estimator for generalized pareto and extreme-value distributions , 1998 .

[10] Richard L. Smith. Extreme Value Analysis of Environmental Time Series: An Application to Trend Detection in Ground-Level Ozone , 1989 .

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

[12] John D Barrett. The Process Evaluation Handbook , 2001, Technometrics.

[13] Richard L. Smith,et al. Models for exceedances over high thresholds , 1990 .

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