Multivariate semi-Weibull distributions

Some multivariate semi-Weibull (denoted by MSW) distributions including the Marshall–Olkin multivariate semi-Weibull (denoted by MO-MSW) one are introduced. They are more general than the multivariate Weibull distributions proposed by Lee [L. Lee, Multivariate distributions having Weibull properties, J. Multivariate Anal. 9 (1979) 267–277]. The Marshall–Olkin multivariate semi-Pareto (denoted by MO-MSP) distribution is also defined. Two characterization theorems for the homogeneous MSW are proved. The multivariate minima domain of partial attraction of MSW is studied, and the interrelationships between MO-MSP and MSW are examined. The MSW distribution possesses the minima-semi-stability and minima-infinite divisibility properties.