gk: An R Package for the g-and-k and generalised g-and-h Distributions

Abstract

The g-and-k and (generalised) g-and-h distributions are flexible univariate distributions which can model highly skewed or heavy tailed data through only four parameters: location and scale, and two shape parameters influencing the skewness and kurtosis. These distributions have the unusual property that they are defined through their quantile function (inverse cumulative distribution function) and their density is unavailable in closed form, which makes parameter inference complicated. This paper presents the gk R package to work with these distributions. It provides the usual distribution functions and several algorithms for inference of independent identically distributed data, including the finite difference stochastic approximation method, which has not been used before for this problem.