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 two-parameter Weibull distribution. Percentiles of three pivotal ratios related to the power-rule model for a two-parameter Weibull distribution are examined. It is shown that the distributions of these pivotal ratios are closely related to appropriate t and χ² distributions. The regression equations given provide approximations to the percentiles of the pivotal ratios in terms of t and χ ² distributions. Such approximations are appropriate in several practical situations where some accuracy can be sacrificed for expediency and tractability