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Some new results on convolutions of heterogeneous gamma random variables

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  • Zhao, Peng
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    Abstract

    Convolutions of independent random variables often arise in a natural way in many applied areas. In this paper, we study various stochastic orderings of convolutions of heterogeneous gamma random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [dispersive order, hazard rate order, star order, right spread order, mean residual life order] between convolutions of two heterogeneous gamma sets of variables wherein they have both differing scale parameters and differing shape parameters. The results established in this paper strengthen and generalize those known in the literature.

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    Bibliographic Info

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

    Volume (Year): 102 (2011)
    Issue (Month): 5 (May)
    Pages: 958-976

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    Handle: RePEc:eee:jmvana:v:102:y:2011:i:5:p:958-976

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    Keywords: Likelihood ratio order Dispersive order Hazard rate order Star order Right spread order Mean residual life order Majorization p-larger order Reciprocal majorization order Gamma convolution;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Zhao, Peng & Hu, Taizhong, 2010. "On hazard rate ordering of the sums of heterogeneous geometric random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 44-51, January.
    2. 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.
    3. Zhao, Peng & Li, Xiaohu & Balakrishnan, N., 2009. "Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 952-962, May.
    4. Furman, Edward, 2008. "On a multivariate gamma distribution," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2353-2360, October.
    5. Kochar, Subhash & Ma, Chunsheng, 1999. "Dispersive ordering of convolutions of exponential random variables," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 321-324, July.
    6. Zhao, Peng & Balakrishnan, N., 2010. "Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 969-974, June.
    7. Sen, Ananda & Balakrishnan, N., 1999. "Convolution of geometrics and a reliability problem," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 421-426, July.
    8. Mi, J. & Shi, W. & Zhou, Y.Y., 2008. "Some properties of convolutions of Pascal and Erlang random variables," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2378-2387, October.
    9. Zhao, Peng & Balakrishnan, N., 2009. "Likelihood ratio ordering of convolutions of heterogeneous exponential and geometric random variables," Statistics & Probability Letters, Elsevier, vol. 79(15), pages 1717-1723, August.
    10. 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.
    11. Zhao, Peng & Balakrishnan, N., 2009. "Mean residual life order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1792-1801, September.
    12. Korwar, Ramesh M., 2002. "On Stochastic Orders for Sums of Independent Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 344-357, February.
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