Likelihood ratio orderings of spacings of heterogeneous exponential random variables
Let X1,X2,...,Xn be independent exponential random variables such that Xi has failure rate [lambda] for i=1,...,p and Xj has failure rate [lambda]* 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[reverse not equivalent]0. It is shown that Di:n(p,q)[less-than-or-equals, slant]lrDi+1:n(p,q) for i=1,...,n-1, and that if [lambda][less-than-or-equals, slant][lambda]* then , and for i=1,...,n, where [less-than-or-equals, slant]lr denotes the likelihood ratio order. The main results are used to establish the dispersive orderings between spacings.
Year of publication: |
2007
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Authors: | Wen, Songqiao ; Lu, Qingshu ; Hu, Taizhong |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 98.2007, 4, p. 743-756
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Publisher: |
Elsevier |
Keywords: | Likelihood ratio order Dispersive order Order statistics Spacings Exponential distributions Permanent |
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