# Gaminv

## Definition:

$gp=gaminv(p, a, b)$ computes the inverse of Gamma cdf at $p$ , with parameters $a$ and $b$.

The deviate,$gp$, associated with the lower tail probability $p$ of the $F$ distribution with $\nu$ degrees of freedom is defined as the solution to

$P(G\leq gp)=p=\frac 1{\beta ^\alpha \Gamma (\alpha )}\int_0^{gp}G^{\alpha -1}e^{-G/\beta }dG$

$0\leq gp<\infty ;\alpha ,\beta >0$.

## Parameters:

$p$ (input, double)
the probability,$p$, from the required Gamma distribution.$0 \le p <1$
$a$ (input, double)
the shape parameter $\alpha$ of the gamma distribution, must be positive($a>0$).
$b$ (input, double)
the scale parameter $\beta$ of the gamma distribution , must be positive($b>0$).
$gp$ (output, double)
the deviate, $g_p$