Some properties and a characterization of trivariate and multivariate binomial distributions

By considering a trivariate binomial distribution, the regression equations are obtained and a set of necessary and sufficient conditions are given for the regression to be linear. Under the limiting conditions, the expressions approach those of trivariate Poisson distribution derived by Mahamunulu (1967). A characterization of the trivariate binomial distribution is also established based on the distribution of the sum of two trivariate random …