Approximations to Weighted Sums of Random Variables

TL;DR

This paper develops error bounds for approximating weighted sums of dependent and independent random variables using Stein's method, with applications in finance and statistics.

Contribution

It introduces new error bounds for binomial and negative binomial approximations to weighted sums of locally dependent variables, extending existing methods.

Findings

Error bounds for binomial approximation

Error bounds for negative binomial approximation

Applications in finance and statistical runs

Abstract

In this paper, we obtain error bound for binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein's method. We also discuss approximation results for weighted sums of independent random variables. We demonstrate our results through some applications in finance and runs in statistics.