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Large deviations for random sums of negatively dependent random variables with consistently varying tails

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  • Chen, Yu
  • Zhang, Weiping

Abstract

Let {Xk,k=1,2,...} be a sequence of negatively dependent random variables with common distribution F and finite expectation [mu]. Under the assumption that the tail probability is consistently varying as x tends to infinity, this paper investigates precise large deviations for the random sum , where {N(t),t[greater-or-equal, slanted]0} is a nonnegative and integer-valued process independent of {Xk,k=1,2,...}.

Suggested Citation

  • Chen, Yu & Zhang, Weiping, 2007. "Large deviations for random sums of negatively dependent random variables with consistently varying tails," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 530-538, March.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:5:p:530-538
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    References listed on IDEAS

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    1. Cline, D. B. H. & Samorodnitsky, G., 1994. "Subexponentiality of the product of independent random variables," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 75-98, January.
    2. Tang, Qihe & Tsitsiashvili, Gurami, 2003. "Precise estimates for the ruin probability in finite horizon in a discrete-time model with heavy-tailed insurance and financial risks," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 299-325, December.
    3. Tang, Qihe & Su, Chun & Jiang, Tao & Zhang, Jinsong, 2001. "Large deviations for heavy-tailed random sums in compound renewal model," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 91-100, March.
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    Cited by:

    1. Kong, Fanchao & Zong, Gaofeng, 2008. "The finite-time ruin probability for ND claims with constant interest force," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 3103-3109, December.
    2. Jong-Il Baek & Sung-Tae Park, 2010. "RETRACTED ARTICLE: Convergence of Weighted Sums for Arrays of Negatively Dependent Random Variables and Its Applications," Journal of Theoretical Probability, Springer, vol. 23(2), pages 362-377, June.

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