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 \(k\) (this is in addition to the prior described by Zhang and Stephens, 2009), 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 (see details in Vehtari et al., 2024). This is used internally but is exported for use by other packages.

Usage

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

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.
weights: An optional numeric vector of positive weights the same length as x. If NULL (the default), all observations are weighted equally and the result is identical to the unweighted fit. Weights are normalized internally to sum to length(x).

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.