Likelihood ratio orderings of spacings of heterogeneous exponential random variables |
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Authors: | Songqiao Wen |
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Affiliation: | Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China |
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Abstract: | Let X1,X2,…,Xn be independent exponential random variables such that Xi has failure rate λ for i=1,…,p and Xj has failure rate λ* for j=p+1,…,n, where p≥1 and q=n-p≥1. Denote by Di:n(p,q)=Xi:n-Xi-1:n the ith spacing of the order statistics , where X0:n≡0. It is shown that Di:n(p,q)?lrDi+1:n(p,q) for i=1,…,n-1, and that if λ?λ* then , and for i=1,…,n, where ?lr denotes the likelihood ratio order. The main results are used to establish the dispersive orderings between spacings. |
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Keywords: | 60E15 62E10 |
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