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Some New Results on Stochastic Comparisons of Spacings from Heterogeneous Exponential Distributions


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  • Kochar, Subhash
  • Rojo, Javier
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    Some new results are obtained on stochastic orderings between random vectors of spacings from heterogeneous exponential distributions and homogeneous ones. LetD1, ..., Dnbe the normalized spacings associated with independent exponential random variablesX1, ...,Xn, whereXihas hazard rate[lambda]i,i=1, 2, ..., n. LetD*1, ..., D*nbe the normalized spacings of a random sampleY1, ..., Ynof sizenfrom an exponential distribution with hazard rate[lambda]=[summation operator]ni=1 [lambda]i/n. It is shown that for anyn[greater-or-equal, slanted]2, the random vector (D1, ..., Dn) is greater than the random vector (D*1, ..., D*n) in the sense of multivariate likelihood ratio ordering. It also follows from the results proved in this paper that for anyjbetween 2 andn, the survival function ofXj:n-X1:nis Schur convex.

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

    Volume (Year): 59 (1996)
    Issue (Month): 2 (November)
    Pages: 272-281

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    Handle: RePEc:eee:jmvana:v:59:y:1996:i:2:p:272-281

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    Keywords: likelihood ratio ordering multivariate likelihood ratio ordering hazard rate ordering Schur functions majorization sample range order statistics;


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    Cited by:
    1. 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.
    2. Ding, Weiyong & Da, Gaofeng & Zhao, Peng, 2013. "On sample ranges from two sets of heterogenous random variables," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 63-73.
    3. 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.
    4. Chu, Yu-Ming & Xia, Wei-Feng & Zhang, Xiao-Hui, 2012. "The Schur concavity, Schur multiplicative and harmonic convexities of the second dual form of the Hamy symmetric function with applications," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 412-421.
    5. Ding, Weiyong & Zhang, Yiying & Zhao, Peng, 2013. "Comparisons of k-out-of-n systems with heterogenous components," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 493-502.
    6. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    7. Paltanea, Eugen, 2011. "Bounds for mixtures of order statistics from exponentials and applications," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 896-907, May.
    8. 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.
    9. Genest, Christian & Kochar, Subhash C. & Xu, Maochao, 2009. "On the range of heterogeneous samples," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1587-1592, September.
    10. Peng Zhao & N. Balakrishnan, 2011. "Dispersive ordering of fail-safe systems with heterogeneous exponential components," Metrika, Springer, vol. 74(2), pages 203-210, September.
    11. 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.
    12. Dolati, Ali & Genest, Christian & Kochar, Subhash C., 2008. "On the dependence between the extreme order statistics in the proportional hazards model," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 777-786, May.


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