Classes of multivariate exponential and multivariate geometric distributions derived from Markov processes
Nicholas Tibor Longford · Lecture notes-monograph series · 1990
We define a class of multivariate exponential distributions as the distributions of occupancy times in upwards skip-free Markov processes in continuous time.These distributions are infinitely divisible, and the multivariate gamma class denned by convolutions and fractions is a substantial generalization of the class defined by Johnson and 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.