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Pré-Publication, Document De Travail Année : 2018

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

Résumé

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.
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Dates et versions

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

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Essomanda Konzou, Angelo Efoévi Koudou. About the Stein equation for the generalized inverse Gaussian and Kummer distributions. 2018. ⟨hal-02412682v2⟩
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