Generalized location-scale mixtures of elliptical distributions: Definitions and stochastic comparisons

This article proposes a unified class of generalized location-scale mixture multivariate elliptical distributions and studies integral stochastic orderings random vectors following such distributions. Given vector Z, independent X Y, the scale parameter this is mixed with function α(Z) its skew another β(Z). Sufficient (and necessary) conditions are established for stochastically comparing different stemming from by means several orders including usual order, convex increasing supermodular some related linear orders. Two insightful assumptions density generators distributions, aiming to control generators’ tail, provided make comparisons among mixed-elliptical vectors. Some applications in applied probability actuarial science also as illustrations on main findings.