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On Stochastic Orders for Sums of Independent Random Variables

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  • Korwar, Ramesh M.
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    Abstract

    In this paper, it is shown that a convolution of uniform distributions (a) is more dispersed and (b) has a smaller hazard rate when the scale parameters of the uniform distributions are more dispersed in the sense of majorization. It is also shown that a convolution of gamma distributions with a common shape parameter greater than 1 is larger in (a) likelihood ratio order and (b) dispersive order when the scale parameters are more dispersed in the sense of majorization.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 80 (2002)
    Issue (Month): 2 (February)
    Pages: 344-357

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    Handle: RePEc:eee:jmvana:v:80:y:2002:i:2:p:344-357

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    Keywords: convolutions dispersive order hazard rate order likelihood ratio order majorization gamma distribution exponential distribution uniform distribution increasing failure rate distribution totally positive of order two function;

    References

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    1. Boland, Philip J. & El-Neweihi, Emad & Proschan, Frank, 1994. "Schur properties of convolutions of exponential and geometric random variables," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 48(1), pages 157-167, January.
    2. Kochar, Subhash & Ma, Chunsheng, 1999. "Dispersive ordering of convolutions of exponential random variables," Statistics & Probability Letters, Elsevier, Elsevier, vol. 43(3), pages 321-324, July.
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    Cited by:
    1. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(3), pages 271-281, February.
    2. Zhao, Peng & Balakrishnan, N., 2009. "Likelihood ratio ordering of convolutions of heterogeneous exponential and geometric random variables," Statistics & Probability Letters, Elsevier, Elsevier, vol. 79(15), pages 1717-1723, August.
    3. Zhao, Peng & Balakrishnan, N., 2010. "Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables," Statistics & Probability Letters, Elsevier, Elsevier, vol. 80(11-12), pages 969-974, June.
    4. Fathi Manesh, Sirous & Khaledi, Baha-Eldin, 2008. "On the likelihood ratio order for convolutions of independent generalized Rayleigh random variables," Statistics & Probability Letters, Elsevier, Elsevier, vol. 78(18), pages 3139-3144, December.
    5. Lu, ZhiYi & Meng, LiLi, 2011. "Stochastic comparisons for allocations of policy limits and deductibles with applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 338-343, May.
    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, Elsevier, vol. 105(1), pages 45-54.
    7. Lihong, Sun & Xinsheng, Zhang, 2005. "Stochastic comparisons of order statistics from gamma distributions," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 93(1), pages 112-121, March.
    8. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, Springer, vol. 47(2), pages 227-247, March.
    9. Zhao, Peng & Balakrishnan, N., 2009. "Mean residual life order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 100(8), pages 1792-1801, September.
    10. Zhao, Peng, 2011. "Some new results on convolutions of heterogeneous gamma random variables," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 102(5), pages 958-976, May.
    11. Zhao, Peng & Hu, Taizhong, 2010. "On hazard rate ordering of the sums of heterogeneous geometric random variables," Journal of Multivariate Analysis, Elsevier, Elsevier, vol. 101(1), pages 44-51, January.

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