Title : ( Nonparametric Confidence Intervals and Tolerance Limits Based on Minima and Maxima )
Authors: Mostafa Razmkhah , Jafar Ahmadi , Bahareh Khatib Astaneh ,
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Abstract
Let Xij 1 ≤ i ≤ k 1 ≤ j ≤ ni be independent random variables and for a fixed iXij ’s, 1 ≤ j ≤ ni be identically distributed random variables with survival function Fi = F i , where i is a known positive constant. Also, suppose Mi and M i , respectively, denote the maximum and minimum of the ith sample. This article investigates the nonparametric confidence intervals for an arbitrary quantile of the distribution F and tolerance limits based on these statistics. Various cases have been studied and in each case, the nonparametric confidence intervals are obtained and exact expressions for the confidence coefficients of these confidence intervals are derived. A data set representing the time of successive failures of the air conditioning system on Boeing 720 jet aircraft is used to illustrate the results. Finally, the accuracy of the proposed procedure has been investigated, when i’s are unknown via a simulation study.
Keywords
Coverage probability; Multisampling plan; Order statistics; Proportional hazard model; Record values
@article{paperid:1008520,
author = {Razmkhah, Mostafa and Ahmadi, Jafar and Khatib Astaneh, Bahareh},
title = {Nonparametric Confidence Intervals and Tolerance Limits Based on Minima and Maxima},
journal = {Communications in Statistics - Theory and Methods},
year = {2008},
volume = {37},
number = {10},
month = {May},
issn = {0361-0926},
pages = {1525--1542},
numpages = {17},
keywords = {Coverage probability; Multisampling plan; Order statistics;
Proportional hazard model; Record values},
}
%0 Journal Article
%T Nonparametric Confidence Intervals and Tolerance Limits Based on Minima and Maxima
%A Razmkhah, Mostafa
%A Ahmadi, Jafar
%A Khatib Astaneh, Bahareh
%J Communications in Statistics - Theory and Methods
%@ 0361-0926
%D 2008
