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Linear Combination of Independent Exponential Random Variables

Author

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  • Kim-Hung Li

    (Asian Cities Research Centre Ltd.)

  • Cheuk Ting Li

    (University of California, Berkeley)

Abstract

In this paper we prove a recursive identity for the cumulative distribution function of a linear combination of independent exponential random variables. The result is then extended to probability density function, expected value of functions of a linear combination of independent exponential random variables, and other functions. Our goal is on the exact and approximate calculation of the above mentioned functions and expected values. We study this computational problem from different views, namely as a Hermite interpolation problem, and as a matrix function evaluation problem. Examples are presented to illustrate the applicability and performance of the methods.

Suggested Citation

  • Kim-Hung Li & Cheuk Ting Li, 2019. "Linear Combination of Independent Exponential Random Variables," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 253-277, March.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9653-0
    DOI: 10.1007/s11009-018-9653-0
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    References listed on IDEAS

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    1. Kordecki, Wojciech, 1997. "Reliability bounds for multistage structures with independent components," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 43-51, May.
    2. René Bekker & Paulien Koeleman, 2011. "Scheduling admissions and reducing variability in bed demand," Health Care Management Science, Springer, vol. 14(3), pages 237-249, September.
    3. Ratanov, Nikita, 2015. "Hypo-exponential distributions and compound Poisson processes with alternating parameters," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 71-78.
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    Cited by:

    1. Schulz, Jan & Mayerhoffer, Daniel M., 2021. "A network approach to consumption," BERG Working Paper Series 173, Bamberg University, Bamberg Economic Research Group.
    2. George P. Yanev, 2020. "Exponential and Hypoexponential Distributions: Some Characterizations," Mathematics, MDPI, vol. 8(12), pages 1-10, December.

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