Stochastic comparisons of order statistics,with applications in relibility |
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| Authors: | Jee Soo Kim Frank Proschan Jayaram Sethuraman |
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| Affiliation: | 1. GTE Laboratories , Waltham, MA, 02154;2. Department of Statistics , Florida State University , Tallahassee, Florida, 32306 |
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| Abstract: | This paper reviews recent developments in the stochastic comparison of order statistics. The results discussed are basically: (l) Stochastic comparisons of linear combinations of order statistics from distributions F and G where G?1 F is convex or starshaped. (2) Stochastic comparisons of individual order statistics and of vectors of order statistics from underlying heterogeneous distributions by the use of majorization and Schur function theory. (3) Stochastic comparison of random processes. Applications to reliability problems are presented illustrating the use and value of the theoretical results described |
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| Keywords: | Stochastic comparison order statistics reliability life testing memorization Schur function heterogeneous distributions k-out-of-n system proportional hazard functions |
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