Bounds for mixtures of order statistics from exponentials and applications
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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Volume (Year): 102 (2011)
Issue (Month): 5 (May)
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References listed on IDEAS
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- Bartoszewicz, Jaroslaw, 2002. "Mixtures of exponential distributions and stochastic orders," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 23-31, March.
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- 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.
- 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.
- 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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