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On perturbations of Stein operator
Authors:A N Kumar  N S Upadhye
Institution:Department of Mathematics, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India
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 for (k1, k2)-events is given.
Keywords:(k1  k2) Distribution  Negative binomial distribution  Perturbation  Probability-generating function  Stein operator  
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