About the Stein equation for the generalized inverse Gaussian and Kummer distributions
ESAIM: Probability and Statistics, Tome 24 (2020), pp. 607-626

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.

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DOI : 10.1051/ps/2020009
Classification : 60F05, 60E05
Keywords: Generalized inverse Gaussian distribution, Kummer distribution, Stein characterization 
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     author = {Konzou, Essomanda and Koudou, Angelo Efoevi},
     title = {About the {Stein} equation for the generalized inverse {Gaussian} and {Kummer} distributions},
     journal = {ESAIM: Probability and Statistics},
     pages = {607--626},
     year = {2020},
     publisher = {EDP Sciences},
     volume = {24},
     doi = {10.1051/ps/2020009},
     mrnumber = {4170177},
     zbl = {1455.60040},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2020009/}
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Konzou, Essomanda; Koudou, Angelo Efoevi. About the Stein equation for the generalized inverse Gaussian and Kummer distributions. ESAIM: Probability and Statistics, Tome 24 (2020), pp. 607-626. doi: 10.1051/ps/2020009

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