• Bernoulli
  • Volume 23, Number 4A (2017), 2828-2859.

On Stein operators for discrete approximations

Neelesh S. Upadhye, Vydas Čekanavičius, and P. Vellaisamy

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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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Bernoulli, Volume 23, Number 4A (2017), 2828-2859.

Received: June 2014
Revised: October 2015
First available in Project Euclid: 9 May 2017

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binomial distribution compound Poisson distribution Panjer’s recursion perturbation Stein’s method total variation norm


Upadhye, Neelesh S.; Čekanavičius, Vydas; Vellaisamy, P. On Stein operators for discrete approximations. Bernoulli 23 (2017), no. 4A, 2828--2859. doi:10.3150/16-BEJ829.

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