Bernoulli

  • 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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Abstract

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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1494316834

Digital Object Identifier
doi:10.3150/16-BEJ829

Mathematical Reviews number (MathSciNet)
MR3648047

Zentralblatt MATH identifier
06778258

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

Citation

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. https://projecteuclid.org/euclid.bj/1494316834


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