Simple Approximate Distributional Results for Confidence and Tolerance Limits for the Weibull Distribution Based on Maximum Likelihood Estimators

One form of the generalized gamma distribution brings out an association between the normal distribution and the extreme-value distribution. This relationship suggests chi-squared, Student's t and noncentral t approximations for certain functions of the maximum likelihood estimators of the parameters of the extreme-value distribution. The accuracy of these approximations is studied by comparing them to existing Monte Carlo simulation results. These approximations provide simple procedures for obtaining approximate confidence intervals for the parameters, tolerance limits, and confidence limits on reliability for the Weibull or extremevalue distribution.