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The joint distribution of the sum and the maximum of heterogeneous exponential random variables

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  • Arendarczyk, Marek
  • Kozubowski, Tomasz. J.
  • Panorska, Anna K.

Abstract

We derive the joint distribution of the sum and the maximum of n independent heterogeneous exponential random variables and provide a detailed description of this new stochastic model for n=2. This generalizes previous results for univariate distributions of the sum and the maximum of heterogeneous exponential random variables as well as their joint distribution in the homogeneous exponential case.

Suggested Citation

  • Arendarczyk, Marek & Kozubowski, Tomasz. J. & Panorska, Anna K., 2018. "The joint distribution of the sum and the maximum of heterogeneous exponential random variables," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 10-19.
    • Handle: RePEc:eee:stapro:v:139:y:2018:i:c:p:10-19
    DOI: 10.1016/j.spl.2018.03.013
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    References listed on IDEAS

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    1. Hua, Lei & Joe, Harry, 2011. "Second order regular variation and conditional tail expectation of multiple risks," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 537-546.
    2. Raluca Vernic, 2011. "Tail Conditional Expectation for the Multivariate Pareto Distribution of the Second Kind: Another Approach," Methodology and Computing in Applied Probability, Springer, vol. 13(1), pages 121-137, March.
    3. Alexandru V. Asimit & Raluca Vernic & Riċardas Zitikis, 2013. "Evaluating Risk Measures and Capital Allocations Based on Multi-Losses Driven by a Heavy-Tailed Background Risk: The Multivariate Pareto-II Model," Risks, MDPI, vol. 1(1), pages 1-20, March.
    4. Kochar, Subhash C & Korwar, Ramesh, 1996. "Stochastic Orders for Spacings of Heterogeneous Exponential Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 69-83, April.
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    Cited by:

    1. Montes, Ignacio & Salamanca, Juan Jesús & Montes, Susana, 2020. "A modified version of stochastic dominance involving dependence," Statistics & Probability Letters, Elsevier, vol. 165(C).
    2. Arendarczyk, Marek & Kozubowski, Tomasz. J. & Panorska, Anna K., 2018. "The joint distribution of the sum and maximum of dependent Pareto risks," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 136-156.

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