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Ordering properties of convolutions of heterogeneous Erlang and Pascal random variables

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  • Zhao, Peng
  • Balakrishnan, N.

Abstract

In this paper, we study ordering properties of convolutions of heterogeneous Erlang and Pascal random variables in terms of the majorization order [p-larger order, reciprocal majorization order] of parameter vectors and the likelihood ratio order [hazard rate order, mean residual life order]. We establish, among other things, that weak majorization order [p-larger order, reciprocal majorization order] between scale parameter vectors and majorization order between shape parameter vectors imply likelihood ratio order [hazard rate order, mean residual life order] between convolutions of two heterogeneous Erlang or Pascal sets of variables. These results strengthen and generalize some of the results known from the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:11-12:p:969-974
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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. 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.
    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. 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.
    5. 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.
    6. 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.
    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. 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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    Cited by:

    1. Zhao, Peng, 2011. "Some new results on convolutions of heterogeneous gamma random variables," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 958-976, May.
    2. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.

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