About the Stein equation for the generalized inverse Gaussian and Kummer distributions - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2019

About the Stein equation for the generalized inverse Gaussian and Kummer distributions

Résumé

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 [A Stein characterisation of the generalized hyperbolic 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. We also bound the first and second derivatives of the Stein equation in the latter case.
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Dates et versions

hal-02412682 , version 2 (04-08-2018)
hal-02412682 , version 1 (15-12-2019)

Identifiants

  • HAL Id : hal-02412682 , version 1

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Essomanda Konzou, Efoevi Angelo Koudou. About the Stein equation for the generalized inverse Gaussian and Kummer distributions. 2019. ⟨hal-02412682v1⟩
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