Volume 24, 2020
|Page(s)||607 - 626|
|Published online||04 November 2020|
About the Stein equation for the generalized inverse Gaussian and Kummer distributions
Université de Lorraine, CNRS, IECL,
2 Université de Lomé, Lomé, Togo.
* Corresponding author: firstname.lastname@example.org
Accepted: 5 February 2020
We observe that the density of the Kummer distribution satisfies a certain differential equation, leading to a Stein characterization of this distribution and to a solution of the related Stein equation. A bound is derived for the solution and for its first and second derivatives. To provide a bound for the solution we partly use the same framework as in Gaunt 2017 [Stein, ESAIM: PS 21 (2017) 303–316] in the case of the generalized inverse Gaussian distribution, which we revisit by correcting a minor error. We also bound the first and second derivatives of the Stein equation in the latter case.
Mathematics Subject Classification: 60F05 / 60E05
Key words: Generalized inverse Gaussian distribution / Kummer distribution / Stein characterization
© The authors. Published by EDP Sciences, SMAI 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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