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.