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Some new Stein operators for product distributions

Abstract : We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent result of \cite{gms18}. This framework applies to non-centered normal and non-centered gamma random variables, as well as a general sub-family of the variance-gamma distributions. Curiously, there is an increase in complexity in the Stein operators for products of independent normals as one moves, for example, from centered to non-centered normals. As applications, we give a simple derivation of the characteristic function of the product of independent normals, and provide insight into why the probability density function of this distribution is much more complicated in the non-centered case than the centered case.
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Contributor : Guillaume Mijoule <>
Submitted on : Wednesday, February 13, 2019 - 1:20:45 PM
Last modification on : Wednesday, February 19, 2020 - 9:00:30 AM

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  • HAL Id : hal-02017801, version 1
  • ARXIV : 1901.11460



Robert E. Gaunt, Guillaume Mijoule, Yvik Swan. Some new Stein operators for product distributions. Brazilian Journal of Probability and Statistics, São Paulo, SP : Associação Brasileira de Estatística, In press. ⟨hal-02017801⟩



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