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, \(g_p\)