A Trivariate F Distribution of Markov Dependent F Distributed Random Variables

The trivariate F distribution comes out with the ratios of the chi- squared random variables. In its classical form it has marginals on xed denominator and arbitrary numerator degrees of freedom parameters. However it was reduced to have marginals on fi xed (or arbitrary) numerator but arbitrary denominator degrees of freedom parameters in the literature. In this paper we introduce a new form which has marginals on both arbitrary numerator and denominator but in the case of Markov dependent random variables. We represent the distribution of those random variables and by means of the joint probability density function we study the bivariate, univariate and conditional distributions. Also some graphics and numerical results for the correlation between the random variables are given.