Abstract
Let X 1, X 2, ..., X n be independent exponential random variables such that X i has failure rate λ for i = 1, ..., p and X j has failure rate λ* for j = p + 1, ..., n, where p ≥ 1 and q = n − p ≥ 1. Denote by D i:n (p,q) = X i:n −X i-1:n the ith spacing of the order statistics X 1:n ≤ X 2:n ≤ ... ≤ X n:n , i = 1, ..., n, where X 0:n ≡ 0. The purpose of this paper is to investigate multivariate likelihood ratio orderings between spacings D i:n (p,q), generalizing univariate comparison results in Wen et al.(J Multivariate Anal 98:743–756, 2007). We also point out that such multivariate likelihood ratio orderings do not hold for order statistics instead of spacings.
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Supported by National Natural Science Foundation of China, the Program for New Century Excellent Talents in University (No.: NCET-04-0569), and by the Knowledge Innovation Program of the Chinese Academy of Sciences (No.: KJCX3-SYW-S02).
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Chen, H., Hu, T. Multivariate likelihood ratio orderings between spacings of heterogeneous exponential random variables. Metrika 68, 17–29 (2008). https://doi.org/10.1007/s00184-007-0140-9
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DOI: https://doi.org/10.1007/s00184-007-0140-9