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On compound sums under dependence

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  • Eryilmaz, Serkan

Abstract

In this paper, we study the compound random variable S=∑t=1NYt when there is a dependence between a random variable N and a sequence of random variables {Yt}t≥1. Such a compound random variable has been found to be useful in several fields including actuarial science, risk management, and reliability. In particular, we develop some results on distributional properties of the random variable S when N is a phase-type random variable that is defined on a sequence of binary trials and depends on {Yt}t≥1. We present illustrative examples and an application for the use of results in actuarial science.

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  • Eryilmaz, Serkan, 2017. "On compound sums under dependence," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 228-234.
    • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:228-234
    DOI: 10.1016/j.insmatheco.2016.12.003
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    1. Fatih Tank & Serkan Eryilmaz, 2015. "The distributions of sum, minima and maxima of generalized geometric random variables," Statistical Papers, Springer, vol. 56(4), pages 1191-1203, November.
    2. Kolev, Nikolai & Paiva, Delhi, 2008. "Random sums of exchangeable variables and actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 147-153, February.
    3. Albrecher, Hansjorg & Boxma, Onno J., 2004. "A ruin model with dependence between claim sizes and claim intervals," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 245-254, October.
    4. Danilenko, Svetlana & Šiaulys, Jonas, 2016. "Randomly stopped sums of not identically distributed heavy tailed random variables," Statistics & Probability Letters, Elsevier, vol. 113(C), pages 84-93.
    5. Koutras, Vasileios M. & Koutras, Markos V. & Yalcin, Femin, 2016. "A simple compound scan statistic useful for modeling insurance and risk management problems," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 202-209.
    6. Eisele, Karl-Theodor, 2006. "Recursions for compound phase distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 149-156, February.
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