Matrix-variate beta distributions are applied in different fields of hypothesis testing, multivariate correlation analysis, zero regression, canonical correlation analysis and etc. A methodology is proposed to generate matrix-variate beta generator distributions by combining the matrix-variate beta kernel with an unknown function of the trace operator. Several statistical characteristics, exten...

Let $p$ be an analytic function defined on the open unit disc $mathbb{D}$ with $p(0)=1.$ The conditions on $alpha$ and $beta$ are derived for $p(z)$ to be subordinate to $1+4z/3+2z^{2}/3=:varphi_{C}(z)$ when $(1-alpha)p(z)+alpha p^{2}(z)+beta zp'(z)/p(z)$ is subordinate to $e^{z}$. Similar problems were investigated for $p(z)$ to lie in a region bounded by lemniscate of Bernoulli $|w^{2}-1|=1$ ...