A New Generalisation of Sam-Solai’s Multivariate symmetric Arcsine Distribution of Kind-1*

Abstract

This paper proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distributions. More specifically the authors visualize a new generalization of Sam-Solai’s Multivariate symmetric arcsine distribution of Kind-1 from the univariate case. Further, we find its Cumulation, Marginal, Conditional distributions, Generating functions and also discussed its special case.The special cases include the transformation of Sam-solai’s Multivariate symmetric arcsine distribution of kind-1 into Multivariate symmetric log arcsine distribution of kind-1 and Multivariate symmetric Inverse arcine distribution of Kind-1. It is found that the conditional variance of Sam-Solai’s Multivariate conditional symmetric arcsine distribution is homoscedastic and the correlation co-efficient among the random variables are similar to Pearson’s product moment correlation co-efficient. Finally area values are obtained for Bi-variate symmetric arcsine distribution of kind-1 and Bivariate probability surfaces and contours are visualized.