Is this a known distribution?

Question

I came across the distribution on $(0,1]$ with the following density function $$f(x) = \frac{2}{\pi}\sqrt{\frac{1}{x}-1}$$

Is this a known distribution? Any references will be appreciated.

Answer 1

This is the beta distribution with pdf

$$f(x,\alpha,\beta) = \frac{x^{\alpha - 1} (1-x)^{\beta - 1}}{C}$$ and parameters $\alpha = \frac{1}{2}$, $\beta = \frac{3}{2}$. (where $C$ is an appropriate constant).