Distribution fit
Normal, Box-Cox, lognormal, 3-parameter lognormal, exponential, 2-parameter exponential, Weibull, 3-parameter Weibull, gamma, logistic, loglogistic, smallest and largest extreme value are fitted by maximum likelihood. Each is scored with the Anderson–Darling statistic with estimated parameters.
Every p-value comes from simulation with a fixed seed, so the same data always give the same answer. For the normal family (normal, lognormal, Box-Cox), A² is compared with its value in 4,000 simulated normal samples of the same size, each with its own estimated mean and standard deviation (above 100 values, samples of 100 stand in; checked at 300, 1,000 and 3,000 values against 100,000 or more simulated samples, this reads p low by up to about 0.015 for p from 0.01 to 0.25, and about 0.005 near p = 0.05). The rest use a parametric bootstrap: simulate the fitted model, refit, and count. A distribution is not rejected when p is at or above α. A high p-value is a weak argument against a model, not proof of it. Every fitted distribution can be used on the capability sheet.