arXiv:1603.07464 Abstract | arXiv Analytics

arXiv:1603.07464 [math.PR]Abstract References Reviews Resources

On Perturbations of Stein Operator

Published 2016-03-24Version 1

In this paper, we obtain Stein operator for sum of $n$ independent random variables (rvs) which is shown as perturbation of negative binomial (NB) operator. Comparing the operator with NB operator, we derive the error bounds for total variation distance by matching parameters. Also, three parameters 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 $(k_1,k_2)$-events is given.

Categories: math.PR

Subjects: 62E17, 62E20, 60E05, 60F05

Keywords: stein operator, perturbation, independent random variables, total variation distance, parameters approximation

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