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