A new generalisation of multivariate Wigner distribution of kind-2

Abstract

In this paper authors proposed a new generalization of family of Sarmanov type Continuous multivariate symmetric probability distributions. Specifically, a new generalization of Multivariate Wigner distribution of kind-2 from the univariate case. Further, we find its Cumulation, Marginal, Conditional distributions, Generating functions and also discussed its special case. The authors derived the generating functions of this distribution in terms of Bessel function. The special cases include the transformation of Multivariate Wigner distribution of Kind-2 into Multivariate log-Wigner distribution of kind-2 and Multivariate Inverse-Wigner distribution of Kind-2. It is found that the conditional variance of Multivariate conditional Wigner distribution is homoscedastic and the population correlation co-efficient among the random variables are similar to Pearson’s population product moment correlation co-efficient. Area values of the bivariate Wigner surface also extracted and visualized.