• A NEW GENERALISATION OF SAM-SOLAI’S MULTIVARIATE ADDITIVE F- DISTRIBUTION OF KIND-2*

Abstract

This paper proposed a new generalization of Sam-Solai’s Multivariate additive F- distribution of Kind-2 from the uni-variate case. Further, we find its Marginal, Multivariate Conditional distributions, Multivariate Generating functions, Multivariate survival, hazard functions and also discussed its special cases. The authors derived the generating functions of this distribution in terms of Whittaker-M function and complex Meijer-G function. The special cases includes the transformation of Sam-Solai’s Multivariate additive F- distribution of Kind -2 into Multivariate additive Beta distribution of Kind-1 of Type-B, Multivariate Beta-distribution of Kind-2 of Type-B, Multivariate Fisher’s Z-distribution of Kind-2 and Multivariate Logistic-F distribution of kind-2. Moreover, it is found that the bi-variate correlation between two F- variables purely depends on the d.f and we simulated and established selected standard bi-variate F- correlation bounds from 10,000 different combination of d.f. The simulation results shows, the correlation between any two F- variables bounded from -1 to +1 for certain combination of fractional d.f.