Approximations Related to the Sums of $m$-dependent Random Variables

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.

Bounds on Negative Binomial Approximation to Call Function

“…(ii) Observe that V can be expressed as a conditional sum of independent rvs and hence, Subsections 5.3 and 5.4 of Röllin [12] can be used to obtain the bound of D(V |•). For more details, see Remarks 3.1(ii) of Kumar et al [10].…”

Approximations to Weighted Sums of Random Variables

“…are mean and variance of binomial and negative binomial distributions, respectively. For more details, we refer the reader to Brown and Xia [3], Eichelsbacher and Reinert [6], Kumar et al [11], Ley et al [12], Upadhye and Barman [18], Upadhye et al [19], and references therein. This paper is organized as follows.…”