Three general multivariate semi-Pareto distributions and their characterizations

Three general multivariate semi-Pareto distributions are developed in this paper. First one--GMP(k)(III) has univariate Pareto (III) marginals, it is characterized by the minimum of two independent and identically distributed random vectors. Second one--GMSP has univariate semi-Pareto marginals and it is characterized by finite sample minima. Third one--MSP is characterized through a geometric minimization procedure. All these three characterizations are based on the general and the particular solutions of the Euler's functional equations of k-variates.