Showing papers by "Palaniappan Vellaisamy published in 2020"
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TL;DR: In this article, the sum of non-negative integer valued random variables and its approximation to the power series distribution was considered and the error bounds for the approximation problem considered were obtained using Stein's method.
Abstract: In this paper, we consider the sums of non-negative integer valued $m$-dependent random variables, and its approximation to the power series distribution. We first discuss some relevant results for power series distribution such as Stein operator, uniform and non-uniform bounds on the solution of Stein equation, and etc. Using Stein's method, we obtain the error bounds for the approximation problem considered. As special cases, we discuss two applications, namely, $2$-runs and $(k_1,k_2)$-runs and compare the bound with the existing bounds.
7 citations
TL;DR: In this paper, a new family of bivariate generalized linear exponential (BGLE) distributions was introduced, whose marginals are generalized linear-exponential distributions (GLE) with respect to the Gaussian distribution.
Abstract: This article introduces a new family of bivariate generalized linear exponential (BGLE) distributions, whose marginals are generalized linear exponential (GLE) distributions. We derive the expressi...
5 citations
TL;DR: A probabilistic interpretation for the Adomian polynomials (AP’s), which is the main part of the ADM, is provided, both for the one-variable and the multivariable case.
Abstract: The Adomian decomposition method (ADM) is a powerful tool to solve several nonlinear functional equations and a large class of initial/boundary value problems. In this paper, we discuss a probabili...
3 citations
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TL;DR: In this paper, the error bounds between Poisson and convolution of power series distributions via Stein's method were obtained, for the total variance distance, and several Poisson limit theorems follow as corollaries from their bounds.
Abstract: In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method This provides a unified approach to many known discrete distributions Several Poisson limit theorems follow as corollaries from our bounds As applications, we compare the Poisson approximation results with the negative binomial approximation results, for the sums of Bernoulli, geometric, and logarithmic series random variables
2 citations
TL;DR: In this article, the main goal of this paper is to establish limit theorems for the sums of dependent Bernoulli random variables, where each successive random variable depends on previous few random variables.
1 citations
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TL;DR: In this article, the authors derived explicit formulas for the n-th order divergence operator in Malliavin calculus in the one-dimensional case and extended these results to the case of isonormal Gaussian space.
Abstract: In this paper, we first derive some explicit formulas for the computation of the n-th order divergence operator in Malliavin calculus in the one-dimensional case. We then extend these results to the case of isonormal Gaussian space. Our results generalize some of the known results for the divergence operator. Our approach in deriving the formulas is new and simple.