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Limiting behaviour of constrained sums of two variables and the principle of a single big jump

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  • Lehtomaa, Jaakko

Abstract

This note studies the asymptotic properties of the variable Zd:=X1d|{X1+X2=d}, as d→∞. Here X1 and X2 are non-negative i.i.d. variables with a common twice differentiable density function f. General results concerning the distributional limits of Zd are discussed with various examples.

Suggested Citation

  • Lehtomaa, Jaakko, 2015. "Limiting behaviour of constrained sums of two variables and the principle of a single big jump," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 157-163.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:157-163
    DOI: 10.1016/j.spl.2015.08.017
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    References listed on IDEAS

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    1. Armendáriz, Inés & Loulakis, Michail, 2011. "Conditional distribution of heavy tailed random variables on large deviations of their sum," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1138-1147, May.
    2. Asmussen, Søren & Klüppelberg, Claudia, 1996. "Large deviations results for subexponential tails, with applications to insurance risk," Stochastic Processes and their Applications, Elsevier, vol. 64(1), pages 103-125, November.
    3. Mihai Banciu & Prakash Mirchandani, 2013. "Technical Note—New Results Concerning Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 61(4), pages 925-931, August.
    4. Martin A. Lariviere, 2006. "A Note on Probability Distributions with Increasing Generalized Failure Rates," Operations Research, INFORMS, vol. 54(3), pages 602-604, June.
    5. Mark Bagnoli & Ted Bergstrom, 2006. "Log-concave probability and its applications," Studies in Economic Theory, in: Charalambos D. Aliprantis & Rosa L. Matzkin & Daniel L. McFadden & James C. Moore & Nicholas C. Yann (ed.), Rationality and Equilibrium, pages 217-241, Springer.
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    Cited by:

    1. Lehtomaa, Jaakko & Resnick, Sidney I., 2020. "Asymptotic independence and support detection techniques for heavy-tailed multivariate data," Insurance: Mathematics and Economics, Elsevier, vol. 93(C), pages 262-277.
    2. Søren Asmussen & Jaakko Lehtomaa, 2017. "Distinguishing Log-Concavity from Heavy Tails," Risks, MDPI, vol. 5(1), pages 1-14, February.

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