New nonparametric tests for testing homogeneity of scale parameters against umbrella alternative

Three nonparametric tests for several sample scale problem against umbrella alternative, when the peak of the umbrella is known, are proposed. The proposed statistics have the advantage of not requiring the several distribution functions to have a common median, but rather any common quantile of order α,0≤α≤1α,0≤α≤1, (not necessarily 1/21/2) which is assumed to be known. The proposed tests are compared with each other in the Pitman asymptotic relative efficiency sense for different distributions.