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Bootstrap prediction and tolerance intervals for the Weibull regression model with censored data
The problems of constructing prediction and tolerance intervals
were considered for Weibull regression models. On the extreme value
distribution scale, the models have the linear form y = Xβ + σ z ,
=NM
where y is the transformed random response vector, X is the nxq
matrix containing values of the regressor variables, β is a vector of
unknown regression coefficients, σ is an unknown scale parameter and
z is a vector of independent standard extreme value distributed error
terms. The intervals constructed include two-sided prediction
intervals and one-sided tolerance intervals. Further, one-sided
confidence bands were developed for percentiles. The interval
procedures can be applied for randomly right-censored data or
uncensored data. Maximum likelihood estimation was used in the
the bootstrap technique for constructing the various intervals.
A simulation study was performed to investigate the accuracy of the
procedures in complete sample cases. From the simulation study, the
bootstrap intervals were found to have accurate confidence levels