La distribuzione binomiale trivariata

In this work the binomial trivariate distribution is defined and studied. It is a generalisation of the binomial bivariate distribution studied by Zenga (1968). Marginal and conditional distributions of the binomial trivariate distribution will be deduced, and, from them, formulae for expectations and variances will be derived.

Several categorical data analyses, consider dichotomous characters imposing either statistical independence or multinomial dependence, ignoring which the natural statistical models of dependence are. The binomial bivariate distribution, defined by Zenga (1968), is the natural structure of the number of successes of two characters in n independent extractions. This work generalises it to three characters: the binomial trivariate distribution, which exhibits univariate margins binomial and bivariate margins binomial bivariate, is defined and studied. Marginal and conditional distributions of the binomial trivariate distribution will be deduced, and, from them, formulae for expectations and variances will be derived.