PERCENTILES OF PIVOTAL RATIOS FOR THE MLE OF THE PARAMETERS OF A WEIBULL REGRESSION-MODEL

The maximum likelihood procedure provides efficient estimators for regression parameters of the power-rule model associated with the 2-parameter Weibull distribution. This paper examines percentiles of three pivotal ratios related to the power-rule model for a 2-parameter Weibull distribution. The distributions of these pivotal ratios are closely related to appropriate t & chi2 distributions as table 1 shows. The regression equations in table 1 provide approximations to the percentiles of the pivotal ratios in terms of t & chi2 distributions. Such approximations are appropriate in several practical situations where some accuracy can be sacrificed for expediency and tractability.