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On the right spread order of convolutions of heterogeneous exponential random variables

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  • Kochar, Subhash
  • Xu, Maochao

Abstract

A sufficient condition for comparing convolutions of heterogeneous exponential random variables in terms of right spread order is established. As a consequence, it is shown that a convolution of heterogeneous independent exponential random variables is more skewed than that of homogeneous exponential random variables in the sense of NBUE order. This gives a new insight into the distribution theory of convolutions of independent random variables. A sufficient condition is also derived for comparing such convolutions in terms of Lorenz order.

Suggested Citation

  • Kochar, Subhash & Xu, Maochao, 2010. "On the right spread order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 165-176, January.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:165-176
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    References listed on IDEAS

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    1. Kochar, Subhash & Ma, Chunsheng, 1999. "Dispersive ordering of convolutions of exponential random variables," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 321-324, July.
    2. Hu, Taizhong & Chen, Jing & Yao, Junchao, 2006. "Preservation of the location independent risk order under convolution," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 406-412, April.
    3. Boland, Philip J. & El-Neweihi, Emad & Proschan, Frank, 1994. "Schur properties of convolutions of exponential and geometric random variables," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 157-167, January.
    4. Subhash C. Kochar & Douglas P. Wiens, 1987. "Partial orderings of life distributions with respect to their aging properties," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(6), pages 823-829, December.
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    Cited by:

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    2. Barmalzan, Ghobad & Payandeh Najafabadi, Amir T., 2015. "On the convex transform and right-spread orders of smallest claim amounts," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 380-384.
    3. You, Yinping & Li, Xiaohu, 2015. "Functional characterizations of bivariate weak SAI with an application," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 225-231.
    4. Zhao, Peng & Zhang, Yiying, 2012. "On sample ranges in multiple-outlier models," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 335-349.
    5. Farbod Roosta-Khorasani & Gábor Székely, 2015. "Schur properties of convolutions of gamma random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(8), pages 997-1014, November.
    6. Balakrishnan, Narayanaswamy & Belzunce, Félix & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 45-54.
    7. Zhang, Yiying & Cheung, Ka Chun, 2020. "On the increasing convex order of generalized aggregation of dependent random variables," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 61-69.

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