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Bounds for mixtures of order statistics from exponentials and applications


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  • Paltanea, Eugen


This paper deals with the stochastic comparison of order statistics and their mixtures. For a random sample of size n from an exponential distribution with hazard rate [lambda], and for 1 0, such that , and let U and V be two random variables with the distribution functions and , respectively. Then, V is greater in the hazard rate order (or the usual stochastic order) than U if and only if , and V is smaller in the hazard rate order (or the usual stochastic order) than U if and only if [lambda]

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

Volume (Year): 102 (2011)
Issue (Month): 5 (May)
Pages: 896-907

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Handle: RePEc:eee:jmvana:v:102:y:2011:i:5:p:896-907

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Keywords: Exponential distribution Order statistics Usual stochastic order Hazard rate order Mixture of distributions;


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  1. Shaked, Moshe & George Shanthikumar, J., 1995. "Hazard rate ordering of k-out-of-n systems," Statistics & Probability Letters, Elsevier, vol. 23(1), pages 1-8, April.
  2. Kochar, Subhash & Rojo, Javier, 1996. "Some New Results on Stochastic Comparisons of Spacings from Heterogeneous Exponential Distributions," Journal of Multivariate Analysis, Elsevier, vol. 59(2), pages 272-281, November.
  3. Navarro, Jorge & Spizzichino, Fabio & Balakrishnan, N., 2010. "Applications of average and projected systems to the study of coherent systems," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1471-1482, July.
  4. Bartoszewicz, Jaroslaw, 2002. "Mixtures of exponential distributions and stochastic orders," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 23-31, March.
  5. 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.
  6. Navarro, Jorge & Rychlik, Tomasz, 2007. "Reliability and expectation bounds for coherent systems with exchangeable components," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 102-113, January.
  7. 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.
  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.
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