Bounds of derivatives of the solution of the Stein equation for the generalized inverse Gaussian and Kummer distributions

Abstract : For regular test functions h, we prove that all the derivatives of the solution of the Stein equation for the generalized inverse Gaussian and Kummer distributions are bounded. In order to complete the results in [6] where the authors have established an upper bound of the solution and its first and second derivatives of the Stein equation for the generalized inverse Gaussian and Kummer distributions, we provide an explicit upper bound of the third derivative of these solutions. Furthermore, for k ≥ 4, by doing a stepwise calculation, we express the bound of the k-th derivative as a function of the bounds of the derivatives of lower order.
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Submitted on : Thursday, December 19, 2019 - 1:11:28 PM
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Essomanda Konzou, Efoévi Koudou, Kossi Gneyou. Bounds of derivatives of the solution of the Stein equation for the generalized inverse Gaussian and Kummer distributions. 2019. ⟨hal-02419186⟩

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