To evaluate F X (x) the parameters, Γ, are needed for the given distribution, or at least an estimate of these Γ. This leads to a set of scenarios (commonly also called cases) where all the parameters or only a (potentially empty) subset of them are known. The present work will operate from the scenario where all parameters are unknown. This entails an estimate of the parameters, which means that Z i = F X (X i ; Γ). Estimation of the parameters is often carried out with methods like maximization of the log-likelihood or in the case of the Cauchy distribution by means of sums of weighted order statistics. For the case of completely unknown parameters the critcal values used to reject the hypothesis of a given distribution depends on the distribution being tested and the size of the data set. Tables of critical values exists, we have used the ones provided by Ref. 82 (Table .26).