Bootstrap prediction and tolerance intervals for the Weibull regression model with censored data

Abstract

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

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