Marshall, Albert W. and Ingram Olkin, "A Multivariate Exponential Distribution", Journal of the American Statistical Association, Vol. 62, No. 317, (March 1967), pp. 30-44.

Abstract: A number of multivariate exponential distributions are known, but they have not been obtained by methods that shed light on their applicability. This paper presents some meaningful derivations of a multivariate exponential distribution that serve to indicate conditions under which the distribution is appropriate. Two of these derivations are based on "shock models," and one is based on the requirement that residual life is independent of age. It is significant that the derivations all lead to the same distribution.

For this distribution, the moment generating function is obtained, comparison is made with the case of independence, the distribution of the minimum is discussed, and various other properties are investigated. A mulivariate Weibull distribution is obtained through a change of variables.