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Product Convolution of Generalized Subexponential Distributions

Author

Listed:
  • Gustas Mikutavičius

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

  • Jonas Šiaulys

    (Institute of Mathematics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
    These authors contributed equally to this work.)

Abstract

Assume that ξ and η are two independent random variables with distribution functions F ξ and F η , respectively. The distribution of a random variable ξ η , denoted by F ξ ⊗ F η , is called the product-convolution of F ξ and F η . It is proved that F ξ ⊗ F η is a generalized subexponential distribution if F ξ belongs to the class of generalized subexponential distributions and η is nonnegative and not degenerated at zero.

Suggested Citation

  • Gustas Mikutavičius & Jonas Šiaulys, 2023. "Product Convolution of Generalized Subexponential Distributions," Mathematics, MDPI, vol. 11(1), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:1:p:248-:d:1023670
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    References listed on IDEAS

    as
    1. Shijie Wang & Yiyu Hu & LianQiang Yang & Wensheng Wang, 2018. "Randomly weighted sums under a wide type of dependence structure with application to conditional tail expectation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(20), pages 5054-5063, October.
    2. Jaunė, Eglė & Šiaulys, Jonas, 2022. "Asymptotic risk decomposition for regularly varying distributions with tail dependence," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Adrian Holhoş, 2021. "On the Approximation by Balázs–Szabados Operators," Mathematics, MDPI, vol. 9(14), pages 1-12, July.
    4. Yang, Yang & Ignatavičiūtė, Eglė & Šiaulys, Jonas, 2015. "Conditional tail expectation of randomly weighted sums with heavy-tailed distributions," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 20-28.
    5. Yang, Yang & Leipus, Remigijus & Šiaulys, Jonas, 2014. "Closure property and maximum of randomly weighted sums with heavy-tailed increments," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 162-170.
    6. Mantas Dirma & Saulius Paukštys & Jonas Šiaulys, 2021. "Tails of the Moments for Sums with Dominatedly Varying Random Summands," Mathematics, MDPI, vol. 9(8), pages 1-26, April.
    7. Yiqing Chen, 2019. "A Renewal Shot Noise Process with Subexponential Shot Marks," Risks, MDPI, vol. 7(2), pages 1-8, June.
    8. Hua, Lei & Joe, Harry, 2014. "Strength of tail dependence based on conditional tail expectation," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 143-159.
    9. Asimit, Alexandru V. & Furman, Edward & Tang, Qihe & Vernic, Raluca, 2011. "Asymptotics for risk capital allocations based on Conditional Tail Expectation," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 310-324.
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