| Issue |
ESAIM: PS
Volume 24, 2020
|
|
|---|---|---|
| Page(s) | 607 - 626 | |
| DOI | https://doi.org/10.1051/ps/2020009 | |
| Published online | 04 November 2020 | |
About the Stein equation for the generalized inverse Gaussian and Kummer distributions
1
Université de Lorraine, CNRS, IECL,
54000
Nancy, France.
2
Université de Lomé,
Lomé, Togo.
* Corresponding author: efoevi.koudou@univ-lorraine.fr
Received:
2
August
2018
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
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