Journal of the Iranian Statistical Society, Volume (6), No (1), Year (2007-3) , Pages (1-16)

#### Title : ( Outer and inner confidence intervals based on extreme order statistics in a proportional hazard model )

Authors: Mostafa Razmkhah , Jafar Ahmadi , Bahareh Khatib Astaneh ,

Citation: BibTeX | EndNote

#### Abstract

Let $M_{i}$ and $M^{\\\'}_{i}$ be the maximum and minimum of the $i$th sample from $k$ independent sample with different sample sizes, respectively. Suppose that the survival distribution function of the $i$-th sample is $\\\\bar{F}_i={\\\\bar{F}}^{\\\\alpha_i}$, where $\\\\alpha_i$ is known and positive constant. It is shown that how various exact non-parametric inferential procedures can be developed on the basis of $M_{i}$\\\'s and $M^{\\\'}_{i}$\\\'s for distribution function $F$ without any assumption about it other than $F$ is continuous. These include confidence intervals for quantiles, outer and inner confidence intervals for quantile intervals and upper and lower confidence limits for quantile differences. Three schemes have been investigated and in each case, the associated confidence coefficients are obtained. A numerical example is given in order to illustrate the proposed procedure.

#### Keywords

Coverage probability; Proportional hazard model; Quantile interval; Quantile difference; Tolerance interval
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@article{paperid:1006781,
author = {Razmkhah, Mostafa and Ahmadi, Jafar and Khatib Astaneh, Bahareh},
title = {Outer and inner confidence intervals based on extreme order statistics in a proportional hazard model},
journal = {Journal of the Iranian Statistical Society},
year = {2007},
volume = {6},
number = {1},
month = {March},
issn = {1726-4057},
pages = {1--16},
numpages = {15},
keywords = {Coverage probability; Proportional hazard model; Quantile interval; Quantile difference; Tolerance interval},
}