A Generator for Generalized Inverse Gaussian Distributions

TL;DR

This paper introduces a novel, efficient sampling algorithm for the generalized inverse Gaussian distribution by decomposing its density and employing adaptive rejection sampling, improving upon existing methods in terms of control and efficiency.

Contribution

The paper presents a new generator for GIG distributions using density decomposition and adaptive rejection sampling, offering improved efficiency and controllability over previous methods.

Findings

The proposed algorithm achieves a controllable rejection rate.

It maintains efficiency across varying parameters and large sample sizes.

The method improves sampling accuracy and setup time.

Abstract

We propose a new generator for the generalized inverse Gaussian (GIG) distribution by decomposing the density of GIG into two components. The first component is a truncated inverse Gamma density, in order to sample from which we improve the traditional inverse CDF method. The second component is the product of an exponential pdf and an inverse Gamma CDF. In order to sample from this quasi-density, we develop a rejection sampling procedure that adaptively adjusts the piecewise proposal density according to the user-specified rejection rate or the desired number of cutoff points. The resulting complete algorithm enjoys controllable rejection rate and moderate setup time. It preserves efficiency for both parameter varying case and large sample case.