Likelihood ratio order of the second order statistic from independent heterogeneous exponential random variables
Let X1,...,Xn be independent exponential random variables with respective hazard rates [lambda]1,...,[lambda]n, and let Y1,...,Yn be independent exponential random variables with common hazard rate [lambda]. This paper proves that X2:n, the second order statistic of X1,...,Xn, is larger than Y2:n, the second order statistic of Y1,...,Yn, in terms of the likelihood ratio order if and only if with . Also, it is shown that X2:n is smaller than Y2:n in terms of the likelihood ratio order if and only if These results form nice extensions of those on the hazard rate order in Pa[caron]lta[caron]nea [E. Pa[caron]lta[caron]nea, On the comparison in hazard rate ordering of fail-safe systems, Journal of Statistical Planning and Inference 138 (2008) 1993-1997].
Volume (Year): 100 (2009)
Issue (Month): 5 (May)
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- 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.
- 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.
- Lillo, Rosa E. & Nanda, Asok K. & Shaked, Moshe, 2001. "Preservation of some likelihood ratio stochastic orders by order statistics," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 111-119, January.
- An, Mark Yuying, 1995.
"Logconcavity versus Logconvexity: A Complete Characterization,"
95-03, Duke University, Department of Economics.
- An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June.
- Belzunce, Félix & Ruiz, José M. & Ruiz, M. Carmen, 2002. "On preservation of some shifted and proportional orders by systems," Statistics & Probability Letters, Elsevier, vol. 60(2), pages 141-154, November.
- Proschan, F. & Sethuraman, J., 1976. "Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability," Journal of Multivariate Analysis, Elsevier, vol. 6(4), pages 608-616, December.
- 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.
- 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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