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- W2022143529 abstract "Let X1:n⩽X2:n⩽⋯⩽Xn:n denote the order statistics of a random sample of size n from a probability distribution with distribution function F. Similarly, let Y1:m⩽Y2:m⩽⋯⩽Ym:m denote the order statistics of an independent random sample of size m from another distribution with distribution function G. We assume that F and G are absolutely continuous with common support (0,∞). The corresponding normalized spacings are defined by Ui:n≡(n−i+1)(Xi:n−Xi−1:n) and Vj:m≡(m−j+1)(Yj:m−Yj−1:m), for i=1,…,n and j=1,…,m, where X0:n=Y0:n≡0. It is proved that if X is smaller than Y in the hazard rate order sense and if either F or G is a decreasing failure rate (DFR) distribution, then Ui:n is stochastically smaller than Vj:m for i⩽j and n−i⩾m−j. If instead, we assume that X is smaller than Y in the likelihood ratio order and if either F or G is DFR, then this result can be strengthened from stochastic ordering to hazard rate ordering. Finally, under a stronger assumption on the shapes of the distributions that either F or G has log-convex density, it is proved that X being smaller than Y in the likelihood ratio order implies that Ui:n is smaller than Vj:m in the sense of likelihood ratio ordering for i⩽j and n−i=m−j." @default.
- W2022143529 created "2016-06-24" @default.
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- W2022143529 date "1999-08-01" @default.
- W2022143529 modified "2023-09-23" @default.
- W2022143529 title "Stochastic orderings between distributions and their sample spacings – II" @default.
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- W2022143529 doi "https://doi.org/10.1016/s0167-7152(99)00004-8" @default.
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