Multivariate Survival Functions with a Min-Stable Property

This paper introduces and studies a class of multivariate survival functions with given univariate marginal G0, called min-stable multivariate G0-distributions, which includes min-stable multivariate exponential distributions as a special case. The representation of the form of Pickands (1981) is derived, and some dependence and other properties of the class are given. The functional form of the class is G0(A), where A is a homogeneous function on Rn+. Conditions are obtained for G0 and A so that a proper multivariate survival function obtains. Interesting special cases are studied including the case where G0 is a Gamma distribution.