About the Stein equation for the generalized inverse Gaussian and Kummer distributions
Probability
2018-08-07 v1 Statistics Theory
Statistics Theory
Abstract
We propose a Stein characterization of the Kummer distribution on (0, ). This result follows from our observation that the density of the Kummer distribution satisfies a certain differential equation, leading to a solution of the related Stein equation. A bound is derived for the solution, under a condition on the parameters. The derivation of this bound is carried out using the same framework as in Gaunt 2017 [A Stein characterisation of the generalized hyper-bolic distribution. ESAIM: Probability and Statistics, 21, 303--316] in the case of the generalized inverse Gaussian distribution, which we revisit by correcting a minor error in the latter paper.
Keywords
Cite
@article{arxiv.1808.01781,
title = {About the Stein equation for the generalized inverse Gaussian and Kummer distributions},
author = {Essomanda Konzou and Angelo Koudou},
journal= {arXiv preprint arXiv:1808.01781},
year = {2018}
}