Corpus ID: 220363781

Approximation Results for Sums of Independent Random Variables.

@article{Kadu2020ApproximationRF,
title={Approximation Results for Sums of Independent Random Variables.},
journal={arXiv: Probability},
year={2020}
}
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 approximation results in total variation distance. The error bounds obtained are either comparable to or improvement over the existing bounds available in the literature. Also, we give an application to the waiting time distribution of 2-runs.
2 Citations

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References

SHOWING 1-10 OF 41 REFERENCES
Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method
• Mathematics
• 1992
The aim of this paper is to extend Stein's method to a compound Poisson distribution setting. The compound Poisson distributions of concern here are those of the form POIS$(\nu)$, where $\nu$ is aExpand
On compound Poisson approximation for sums of random variables
• Mathematics
• 1999
An upper bound for the total variation distance between the distribution of the sum of a sequence of r.v.'s and that of a compound Poisson is derived. Its applications to a general independentExpand
On Stein operators for discrete approximations
• Mathematics
• 2014
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 negativeExpand
On bounds in Poisson approximation for distributions of independent negative-binomial distributed random variables
• Computer Science, Medicine
• SpringerPlus
• 2016
Abstract Using the Stein–Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables areExpand
KERSTAN'S METHOD FOR COMPOUND POISSON APPROXIMATION
We consider the approximation of the distribution of the sum of independent but not necessarily identically distributed random variables by a compound Poisson distribution and also by a finite signedExpand
On Negative Binomial Approximation
• Mathematics
• 2013
This paper deals with negative binomial approximation to sums of independent ${\bf Z}_+$-valued random variables. Stein's method is employed to obtain the error bounds. Convolution of negativeExpand
Poisson approximation for some statis-tics based on exchangeable trials
• Mathematics
• 1983
Stein's (1970) method of proving limit theorems for sums of dependent random variables is used to derive Poisson approximations for a class of statistics, constructed from finitely exchangeableExpand
On perturbations of Stein operator
• Mathematics
• 2016
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 theExpand
Approximations to the distribution of sum of independent non-identically gamma random variables
Calculating the sum of independent non-identically distributed random variables is necessary in the scientific field. Computing the probability of the corresponding significance point is important inExpand
SADDLE POINT APPROXIMATION FOR THE DISTRIBUTION OF THE SUM OF INDEPENDENT RANDOM VARIABLES
• Mathematics
• 1980
In the present paper a uniform asymptotic series is derived for the probability distribution of the sum of a large number of independent random variables. In contrast to the usual Edgeworth-typeExpand