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,\(f_p\).