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November 2017 On Stein operators for discrete approximations
Neelesh S. Upadhye, Vydas Čekanavičius, P. Vellaisamy
Bernoulli 23(4A): 2828-2859 (November 2017). DOI: 10.3150/16-BEJ829


In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, the Stein operators for certain compound distributions, where the random summand satisfies Panjer’s recurrence relation, are derived. A well-known perturbation approach for Stein’s method is used to obtain total variation bounds for the distributions mentioned above. The importance of such approximations is illustrated, for example, by the binomial convoluted with Poisson approximation to sums of independent and dependent indicator random variables.


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Neelesh S. Upadhye. Vydas Čekanavičius. P. Vellaisamy. "On Stein operators for discrete approximations." Bernoulli 23 (4A) 2828 - 2859, November 2017.


Received: 1 June 2014; Revised: 1 October 2015; Published: November 2017
First available in Project Euclid: 9 May 2017

zbMATH: 06778258
MathSciNet: MR3648047
Digital Object Identifier: 10.3150/16-BEJ829

Keywords: Binomial distribution , compound Poisson distribution , Panjer’s recursion , perturbation , Stein’s method , total variation norm

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability


Vol.23 • No. 4A • November 2017
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