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A new proof for the peakedness of linear combinations of random variables

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  • Ju, Shan
  • Pan, Xiaoqing

Abstract

A new proof is given to compare linear combinations of independent and possibly non-identically distributed random variables, as well as bivariate SAI random variables in the sense of peakedness order. The main results extend those given in Proschan (1965) and Ma (1998).

Suggested Citation

  • Ju, Shan & Pan, Xiaoqing, 2016. "A new proof for the peakedness of linear combinations of random variables," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 93-98.
    • Handle: RePEc:eee:stapro:v:114:y:2016:i:c:p:93-98
    DOI: 10.1016/j.spl.2016.03.012
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    References listed on IDEAS

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    1. Pan, Xiaoqing & Yuan, Min & Kochar, Subhash C., 2015. "Stochastic comparisons of weighted sums of arrangement increasing random variables," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 42-50.
    2. Ibragimov, Rustam, 2007. "Efficiency Of Linear Estimators Under Heavy-Tailedness: Convolutions Of Α-Symmetric Distributions," Econometric Theory, Cambridge University Press, vol. 23(3), pages 501-517, June.
    3. Cai, Jun & Wei, Wei, 2015. "Notions of multivariate dependence and their applications in optimal portfolio selections with dependent risks," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 156-169.
    4. Boland, Philip J. & Proschan, Frank, 1988. "Multivariate arrangement increasing functions with applications in probability and statistics," Journal of Multivariate Analysis, Elsevier, vol. 25(2), pages 286-298, May.
    5. Ibragimov, Rustam, 2007. "Efficiency of linear estimators under heavy-tailedness: convolutions of [alpha]-symmetric distributions," Scholarly Articles 2623749, Harvard University Department of Economics.
    6. Cai, Jun & Wei, Wei, 2014. "Some new notions of dependence with applications in optimal allocation problems," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 200-209.
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    Cited by:

    1. Di Lascio, F. Marta L. & Giammusso, Davide & Puccetti, Giovanni, 2018. "A clustering approach and a rule of thumb for risk aggregation," Journal of Banking & Finance, Elsevier, vol. 96(C), pages 236-248.

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