An algebra of Stein operators

Robert Gaunt, Guillaume Mijoule, Yvik Swan

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We build upon recent advances on the distributional aspect of Stein’s method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We show that our results are valid for a wide class of distributions including normal, beta, variance-gamma, generalized gamma and many more. Our operators are kth degree differential operators with polynomial coefficients; they are straightforward to obtain even when the target density bears no explicit handle. As an application, we derive a new formula for the density of the product of k independent symmetric variance-gamma distributed random variables.
    Original languageEnglish
    Pages (from-to)260-279
    JournalJournal of Mathematical Analysis and Applications
    Volume469
    Issue number1
    Early online date11 Sept 2018
    DOIs
    Publication statusPublished - 1 Jan 2019

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