Asymptotic Results for Goodness-of-Fit Statistics with Unknown Parameters

Abstract

Percentage points are given for the asymptotic distributions of the goodness-of-fit statistics $W^2, U^2$ and $A^2$, for the cases where the distribution tested is (a) normal, with mean or variance, or both, unknown; (b) exponential, with scale parameter unknown. Some exact means and variances are also given. The distributions can be expressed as a sum of weighted chi-square variables; the weights are calculated, and the higher cumulants can then be found. The first four cumulants are used to approximate the distributions and give the percentage points.