3.5.3.5.4 Finv

Definition:

f_p=finv(p, df1, df2) computes the inverse of F cdf at  p, with parameters df1 and df2 .

The deviate, f_p, associated with the lower tail probability  p of the F distribution with \nu_1 and \nu_2 degrees of freedom is defined as the solution to

P(F\leq f_p)=p= \frac{\nu _1^{\nu _{1/2}}\nu _2^{\nu _2/2}\Gamma ((\nu _1+\nu _2)/2)}{\Gamma (\nu _1/2)\Gamma (\nu _2/2)}\int_0^{f_p}F^{(\nu _1-2)/2}(\nu _1F+\nu _2)^{-(\nu _1+\nu _2)/2}dF

where

\nu_1,\nu_2 > 0 ;   0 \le f_p < \infty

Parameters:

p (input, double)
the probability,p, from the required F-distribution. 0 \le p<1
df1 (input, double)
the degrees of freedom of the numerator variance, \nu_1, must be positive (df1>0 ).
df2 (input, double)
the degrees of freedom of the denominator variance, \nu_2, must be positive(df2>0).
f_p (output, double)
the deviate,f_p.