| Abstract: | A family of trivariate binomial mixtures with respect to their exponent parameter is introduced and its structure is studied by the use of probability generating functions. Expressions for probabilities, factorial moments and factorial cumulants are given. Conditional distributions are also examined. Illustrative examples include the trivariate Poisson, binomial, negative binomial and modified logarithmic series distributions. In addition, properties of the compounded trivariate Poisson distribution are discussed. Finally biological, medical and ecological applications are indicated. |
