# On perturbations of Stein operator

@article{Kumar2016OnPO, title={On perturbations of Stein operator}, author={A. N. Kumar and N. S. Upadhye}, journal={Communications in Statistics - Theory and Methods}, year={2016}, volume={46}, pages={9284 - 9302} }

ABSTRACT In this article, we obtain a Stein operator for the sum of n independent random variables (rvs) which is shown as the perturbation of the negative binomial (NB) operator. Comparing the operator with NB operator, we derive the error bounds for total variation distance by matching parameters. Also, three-parameter approximation for such a sum is considered and is shown to improve the existing bounds in the literature. Finally, an application of our results to a function of waiting time… Expand

#### 9 Citations

Approximation Results for Sums of Independent Random Variables.

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In this article, we consider Poisson and Poisson convoluted geometric approximation to the sums of $n$ independent random variables under moment conditions. We use Stein's method to derive the… Expand

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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… Expand

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In this paper, we develop Stein’s method for negative binomial distribution using call function defined by fz(k) = (k − z) + = max{k − z, 0}, for k ≥ 0 and z ≥ 0. We obtain error bounds between… Expand

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In this paper, some erroneous results for a dependent setup arising from independent sequence of Bernoulli trials are corrected. Next, a Stein operator for discrete Gibbs measure is derived using PGF… Expand

PR ] 2 6 Se p 20 16 Pseudo-binomial Approximation to ( k 1 , k 2 )-runs

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A k-dependent setup arising from independent sequence of Bernoulli trials is considered and a Stein operator for this setup is obtained which is shown as a perturbation of pseudo-binomial operator.… Expand

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In this article, Stein’s method and z-functions are used to determine a non-uniform bound for approximating the cumulative distribution function of a nonnegative integer-valued random variable X by… Expand

PR ] 2 A ug 2 01 9 On Discrete Gibbs Measure Approximation to Runs

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Runs and patterns is an important topic in the areas related to probability and statistics, such as reliability theory, meteorology and agriculture, statistical testing and quality control among many… Expand

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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… Expand

Pseudo-binomial approximation to (k1,k2)-runs

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Abstract The distribution of ( k 1 , k 2 ) -runs is well-known (Dafnis et al., 2010), under independent and identically distributed (i.i.d.) setup of Bernoulli trials but is intractable under non… Expand

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