Characterizations and closure under convolution of two classes of multivariate life distributions

Let [theta]([eta]) be the class of positive random vectors T for which min1[less-than-or-equals, slant]i[less-than-or-equals, slant]n [alpha]iTi is IFRA (NBU) for all [alpha]i > 0, i = 1,...,n where n is an arbitrary positive integer. Characterizations of the classes [theta] and [eta] are obtained and utilized to show that [eta] is closed under convolution and that [theta] is closed under convolution provided one of the two convoluted vectors has independent components.