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Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables

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  • Xin Gao
  • Hong Xu
  • Dong Ye

Abstract

We consider the asymptotic behavior of a probability density function for the sum of any two lognormally distributed random variables that are nontrivially correlated. We show that both the left and right tails can be approximated by some simple functions. Furthermore, the same techniques are applied to determine the tail probability density function for a ratio statistic, and for a sum with more than two lognormally distributed random variables under some stricter conditions. The results yield new insights into the problem of characterization for a sum of lognormally distributed random variables and demonstrate that there is a need to revisit many existing approximation methods.

Suggested Citation

  • Xin Gao & Hong Xu & Dong Ye, 2009. "Asymptotic Behavior of Tail Density for Sum of Correlated Lognormal Variables," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-28, August.
    • Handle: RePEc:hin:jijmms:630857
    DOI: 10.1155/2009/630857
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    Cited by:

    1. Jo, Wooseok & Lee, Seung Jun, 2024. "Human reliability evaluation method covering operator action timing for dynamic probabilistic safety assessment," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    2. Jochen Ranger & Christoph König & Benjamin W. Domingue & Jörg-Tobias Kuhn & Andreas Frey, 2024. "A Multidimensional Partially Compensatory Response Time Model on Basis of the Log-Normal Distribution," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 431-464, June.
    3. Asli Ozen & Yariv Marmor & Thomas Rohleder & Hari Balasubramanian & Jeanne Huddleston & Paul Huddleston, 2016. "Optimization and Simulation of Orthopedic Spine Surgery Cases at Mayo Clinic," Manufacturing & Service Operations Management, INFORMS, vol. 18(1), pages 157-175, February.
    4. Xiaoou Li & Jingchen Liu & Gongjun Xu, 2016. "On the Tail Probabilities of Aggregated Lognormal Random Fields with Small Noise," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 236-246, February.
    5. Moses Ekpenyong, 2011. "QoS Reliability in GPRS Systems," Modern Applied Science, Canadian Center of Science and Education, vol. 5(2), pages 1-57, April.

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