Characterizations of the General Multivariate Weibull Distributions

A general multivariate Weibull distribution is introduced in this article. The GMW is constructed by a well-defined exponent Radon measure which is satisfied by a functional equation with some assumptions. There is rarely literature published regarding the study of characterization of the multivariate Weibull distribution. Yeh (2009) investigated two characterizations on homogeneous multivariate semi-Weibull distribution. Many characterization theorems of the GMW are proved in this article. All these characterizations lead to a multivariate functional equation. Finally, the limiting distribution of the normalized geometric minima of the GMW is discerned as the general multivariate Pareto distribution.