AbstractFor eachn,X1(n),…,Xn(n) are independent and identically distributed random variables, each with cumulative distribution functionF(x) which is known to be absolutely continuous but is otherwise unknown. The problem is to test the hypothesis that\documentclass{article}\pagestyle{empty}\begin{document}$ F(x) = G\left( {{\textstyle{{x - \theta _1 } \over {\theta _2 }}}} \right) $\end{document}, where the cumulative distribution functionGxis completely specified and satisfies certain regularity conditions, and the parameters θ1, θ2are unknown and unspecified, except that the scale parameter θ2, is positive.Y1(n) ≦Y2(n) ≦ … ≦Yn(n)are the ordered values ofX1(n),…,Xn(n). A test based on a certain subset of {Yi(n)} is proposed, is shown to have asymptotically a normal distribution when the hypothesis is true, and is shown to be consistent against all alternatives satisfying a mild regula