On testing a shape parameter in the presence of a location and a scale parameter

A test on a shape parameter in the presence of two nuisance parameters (a location parameter μ and a scale parameter σ)is proposed. Explicit formulas and approximations are given for three applications where the general and restricted distributions are:Student-vs-Gauss-distribution, λ-vs logistic distribution, and type Iior III vs. type I distribution of largest extremes. The last application can be translated in to the situation of smallest extremes;a numerical example is given in which the hypothesis to be tested states that the data come from a 2-parameter weibull distribution. Critical values of the test and its power for some alternatives are obtained by simulation methods.