Estimate parameters of the Generalized Pareto distribution

Given a sample \(x\), Estimate the parameters \(k\) and \(\sigma\) of the generalized Pareto distribution (GPD), assuming the location parameter is 0. By default the fit uses a prior for \(k\), which will stabilize estimates for very small sample sizes (and low effective sample sizes in the case of MCMC samples). The weakly informative prior is a Gaussian prior centered at 0.5.

Usage

gpdfit(x, wip = TRUE, min_grid_pts = 30, sort_x = TRUE)

Arguments

x: A numeric vector. The sample from which to estimate the parameters.
wip: Logical indicating whether to adjust \(k\) based on a weakly informative Gaussian prior centered on 0.5. Defaults to TRUE.
min_grid_pts: The minimum number of grid points used in the fitting algorithm. The actual number used is min_grid_pts + floor(sqrt(length(x))).
sort_x: If TRUE (the default), the first step in the fitting algorithm is to sort the elements of x. If x is already sorted in ascending order then sort_x can be set to FALSE to skip the initial sorting step.

Value

A named list with components k and sigma.

Details

Here the parameter \(k\) is the negative of \(k\) in Zhang & Stephens (2009).

References

Zhang, J., and Stephens, M. A. (2009). A new and efficient estimation method for the generalized Pareto distribution. Technometrics 51, 316-325.