Two-Parameter Pareto Distribution

Abstract

The Pareto distribution was introduced by Pickands (1975) and has since been applied to a number of areas including socio-economic phenomena, physical and biological processes (Saksena and Johnson, 1984), reliability studies and the analysis of environmental extremes. Davison and Smith (1990) pointed out that the Pareto distribution might form the basis of a broad modeling approach to high-level exceedances. DuMouchel (1983) applied it to estimate the stable index a to measure tail thickness, whereas Davison (1984a, 1984b) modeled contamination due to long-range atmospheric transport of radionuclides. van Montfort and Witter (1985, 1986, 1991) applied the Pareto distribution to model the peaks over threshold (POT) streamflows and rainfall series, and Smith (1984, 1987) applied it to analyze flood frequencies. Similarly, Joe (1987) employed it to estimate quantiles of the maximum of a set of observations. Wang (1991) applied it to develop a peak over threshold (POT) model for flood peaks with Poisson arrival time, whereas Rosbjerg et al. (1992) compared the use of the 2-parameter Pareto and exponential distributions as distribution models for exceedances with the parent distribution being a generalized Pareto distribution. In an extreme value analysis of the flow of Burbage Brook, Barrett (1992) used the Pareto distribution to model the POT flood series with Poisson interarrival times. Davison and Smith (1990) presented a comprehensive analysis of the extremes of data by use of the Pareto distribution for modeling the sizes and occurrences of exceedances over high thresholds.