If the survival function
satisfies the functional equation
![](//static.cambridge.org/content/id/urn%3Acambridge.org%3Aid%3Aarticle%3AS0021900200037499/resource/name/S0021900200037499_eqn1.gif?pub-status=live)
where e = (1, …, 1), and if the marginal distributions are exponential, then
is the multivariate exponential distribution of Marshall and Olkin. The functional equation has many solutions if the requirement of exponential marginals is not imposed, but the class of possible marginals is somewhat limited (e.g., marginals must be absolutely continuous). The class of possible solutions of the equation is characterized in this paper, and several examples are obtained from models for dependence that may be of practical interest.