Approximations of the cumulative distribution function for infinite weighted sum of random variables

X. Shi, A. Wong and S. Zheng

Statistics & Probability Letters, 2019, vol. 155, issue C, -

Abstract: The infinite weighted sum of random variables originates from the linear process, random walk, and series representation of Brownian motion and stochastic integral in goodness-of-fit test. In general, this infinite weighted sum of random variables is approximated by the truncated one-term approximation. However, it is very time consuming to numerically obtain the cumulative distribution of the truncated one-term approximation with high accuracy. In this paper, a truncated two-term approximation is proposed, which significantly reduced the required computational time while maintaining high accuracy of approximating the cumulative distribution of the infinite weighted sum of random variables. Three examples are used to demonstrate the simplicity and accuracy of the proposed method.

Keywords: Brownian motion; Infinite sum; Linear process; Random walk; Stochastic integral; Truncated two-term approximation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spl.2019.108567

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