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Stochastic comparisons of order statistics from gamma distributions

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  • Lihong, Sun
  • Xinsheng, Zhang

Abstract

Let (X1,X2,...,Xn) and (Y1,Y2,...,Yn) be gamma random vectors with common shape parameter [alpha] (0 1, we can only compare the the first- and last-order statistics. Some earlier results on stochastically comparing proportional hazard functions are shown to be special cases of our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:1:p:112-121
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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.
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    6. 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.
    7. Chang, Kuo-Hwa, 2001. "Stochastic orders of the sums of two exponential random variables," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 389-396, February.
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    Cited by:

    1. Fischer, T. & Balakrishnan, N. & Cramer, E., 2008. "Mixture representation for order statistics from INID progressive censoring and its applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 1999-2015, October.
    2. Torrado, Nuria & Lillo, Rosa E., 2013. "Likelihood ratio order of spacings from two heterogeneous samples," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 338-348.
    3. Zhao, Peng & Balakrishnan, N., 2011. "New results on comparisons of parallel systems with heterogeneous gamma components," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 36-44, January.
    4. Misra, Neeraj & Misra, Amit Kumar, 2013. "On comparison of reversed hazard rates of two parallel systems comprising of independent gamma components," Statistics & Probability Letters, Elsevier, vol. 83(6), pages 1567-1570.
    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.

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