3.5.3.5.5 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