Confidence Intervals

Confidence intervals are computed for all model parameters and are reported in the "Analysis of Parameter Estimates" table. The confidence coefficient can be specified with the ALPHA= MODEL statement option, resulting in a two-sided confidence coefficient. The default confidence coefficient is 95, corresponding to .

Regression Parameters

A two-sided confidence interval for the regression parameter is based on the asymptotic normality of the maximum likelihood estimator and is computed by

     
     

where is the estimated standard error of , and is the percentile of the standard normal distribution.

Scale Parameter

A two-sided confidence interval for the scale parameter in the location-scale model is based on the asymptotic normality of the logarithm of the maximum likelihood estimator , and is computed by

     
     

Refer to Meeker and Escobar (1998) for more information.

Weibull Scale and Shape Parameters

The Weibull distribution scale parameter and shape parameter are obtained by transforming the extreme-value location parameter and scale parameter :

     
     

Consequently, two-sided confidence intervals for the Weibull scale and shape parameters are computed as

     
     

Gamma Shape Parameter

A two-sided confidence interval for the three-parameter gamma shape parameter is computed by