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

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Listed:
  • Shi, X.
  • Wong, A.
  • Zheng, S.

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.

Suggested Citation

  • Shi, X. & Wong, A. & Zheng, S., 2019. "Approximations of the cumulative distribution function for infinite weighted sum of random variables," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:155:y:2019:i:c:11
    DOI: 10.1016/j.spl.2019.108567
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    References listed on IDEAS

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    1. Sargan, J D & Mikhail, W M, 1971. "A General Approximation to the Distribution of Instrumental Variables Estimates," Econometrica, Econometric Society, vol. 39(1), pages 131-169, January.
    2. Andrey Feuerverger, 2016. "On Goodness of Fit for Operational Risk," International Statistical Review, International Statistical Institute, vol. 84(3), pages 434-455, December.
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