By considering pointwise maxima of independent stationary random processes with dependent Cauchy marginals, we define a new process whose univariate limit distributions are Fréchet and the bivariate distributions interpolate between independence and complete dependence. The limiting dependence...

We characterize uniform distributions on spheres in n-dimensional spacesL[alpha]by certain Cauchy-like (n-1)-dimensional distributions of the quotients and derive some properties of mixtures of uniform distributions on such spheres, i.e.,[alpha]-spherical distributions. We feel that a simple...

Consider a general linear model Y=X[beta]+Z where Cov Z may be known only partially. We investigate carefully the notions of sufficiency, ancillarity, invariance, and equivariance and related notions for projectors in a general linear model. In this way we can prove a Basu type theorem. This...