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Dispersive ordering of convolutions of exponential random variables

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  • Kochar, Subhash
  • Ma, Chunsheng

Abstract

Let X[lambda]1,...,X[lambda]n be independent random variables such that X[lambda]i has exponential distribution with hazard rate [lambda]i, i=1,...,n. It is shown that [summation operator]i=1nX[lambda]i is more dispersed than [summation operator]i=1nX[lambda]i* if ([lambda]1,...,[lambda]n) majorizes ([lambda]1*,...,[lambda]n*).

Suggested Citation

  • Kochar, Subhash & Ma, Chunsheng, 1999. "Dispersive ordering of convolutions of exponential random variables," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 321-324, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:3:p:321-324
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    References listed on IDEAS

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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, vol. 48(1), pages 157-167, January.
    2. Kochar, Subhash C & Korwar, Ramesh, 1996. "Stochastic Orders for Spacings of Heterogeneous Exponential Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 57(1), pages 69-83, April.
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    Citations

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    Cited by:

    1. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    2. 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.
    3. 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.
    4. Longxiang Fang & N. Balakrishnan, 2016. "Likelihood ratio order of parallel systems with heterogeneous Weibull components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 693-703, August.
    5. 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.
    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. 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.
    8. 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.
    9. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 271-281, February.
    10. Fathi Manesh, Sirous & Khaledi, Baha-Eldin, 2008. "On the likelihood ratio order for convolutions of independent generalized Rayleigh random variables," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3139-3144, December.
    11. Lihong, Sun & Xinsheng, Zhang, 2005. "Stochastic comparisons of order statistics from gamma distributions," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 112-121, March.
    12. 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.
    13. Fang, Longxiang & Zhang, Xinsheng, 2013. "Stochastic comparisons of series systems with heterogeneous Weibull components," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1649-1653.
    14. 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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