Parameter and Quantile Estimation for the Generalized Pareto Distribution

1987/08/01 by J. R.M. Hosking, J. R. M. Hosking, J. R. Wallis +1 · 8 citations
Decision Sciences · Economics, Econometrics and Finance · Environmental Science · Mathematics · #Applied mathematics #Distribution (mathematics) #Estimator #Exponential distribution #Extreme value theory #Financial Risk and Volatility Modeling #Generalized Pareto distribution #Hydrology and Drought Analysis #Lomax distribution #Mathematical analysis #Mathematical optimization #Mathematics #Pareto distribution #Pareto interpolation #Pareto principle #Probabilistic and Robust Engineering Design #Quantile #Statistics

paper · doi:10.1080/00401706.1987.10488243

openalex publication_date 1987/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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.

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