I've been reading a paper for self study on the beta-egarch model here: https://core.ac.uk/download/pdf/42337476.pdf
One of the things I don't understand is how the following:
$$ b_{t}=\frac{(y_{t}-\mu)^{2}/\left[\nu \exp(2\lambda_{t|t-1})\right]}{1+(y_{t}-\mu)^{2}/\left[\nu \exp(2\lambda_{t|t-1})\right]} $$
is a $B(\frac{1}{2},\frac{\nu}{2})$
My initial idea was $$ \left(1+(y_{t}-\mu)^{2}/\left[\nu \exp(2\lambda_{t|t-1})\right]\right)^{??-1}.\left((y_{t}-\mu)^{2}/\left[\nu \exp(2\lambda_{t|t-1})\right]\right)^{??-1} $$
but even then, I don't understand how to arise to the powers of required beta distribution.
Any help appreciated