Non-Central Beta Type 3 Distribution

Let $X$ and $Y$ be independent random variables, $X$ having a gamma distribution with shape parameter $a$ and $Y$ having a non-central gamma distribution with shape and non-centrality parameters $b$ and $delta$, respectively. Define $ W ={X}/(X + 2 Y)$. Then, the random variable $W$ has a non-central beta type 3 distribution, $Wsim extnormal{NCB3} (a,b;delta)$. In this article we study several of its properties. We also give a multivariate generalization of the non-central beta type 3 distribution and derive its properties.