If the GAMMA, LOGNORMAL, WEIBULL or SU distribution option is specified on the HISTOGRAM statement in PROC CAPABILITY, the degrees of freedom and p-value for the chi-square goodness of fit statistic will be incorrect when the THETA=EST distribution suboption is also specified. The correct degrees of freedom are equal to the number of histogram bins, minus the number of estimated parameters, minus 1. With THETA=EST, the degrees of freedom are not decreased by 1 for the additional estimated parameter.

For the Johnson SU distribution, the degrees of freedom and p-value will be similarly incorrect when the THETA= option is omitted, since by default theta is estimated for this distribution when it is not specified.

There is no circumvention for this problem. It should be noted, however, that the chi-square goodness-of-fit test depends on the number of histograms bin. The empirical distribution function (EDF) goodness-of-fit tests produced by PROC CAPABILITY are invariant to the number of histogram bins and are recommended over the chi-square goodness-of-fit test.