A class of multivariate exponential distributions as the distributions of occupancy times in upwards skip-free Markov processes in continuous time is defined. These distributions are infinitely divisible, and the multivariate Gamma class defined by convolutions and fractions is a substantial generalization of the class defined by Johnson & Kotz (1972). Parallel classes of multivariate geometric and multivariate negative binomial distributions are constructed from occupancy times in 'instant' upwards skip-free Markov chains. Maximum likelihood estimation and times series applications are discussed. (19pp.)
