scipy.special.fdtri¶
- scipy.special.fdtri(dfn, dfd, p) = <ufunc 'fdtri'>¶
The p-th quantile of the F-distribution.
This function is the inverse of the F-distribution CDF,
fdtr, returning the x such that fdtr(dfn, dfd, x) = p.- Parameters
- dfnarray_like
First parameter (positive float).
- dfdarray_like
Second parameter (positive float).
- parray_like
Cumulative probability, in [0, 1].
- Returns
- xndarray
The quantile corresponding to p.
Notes
The computation is carried out using the relation to the inverse regularized beta function, \(I^{-1}_x(a, b)\). Let \(z = I^{-1}_p(d_d/2, d_n/2).\) Then,
\[x = \frac{d_d (1 - z)}{d_n z}.\]If p is such that \(x < 0.5\), the following relation is used instead for improved stability: let \(z' = I^{-1}_{1 - p}(d_n/2, d_d/2).\) Then,
\[x = \frac{d_d z'}{d_n (1 - z')}.\]Wrapper for the Cephes [1] routine
fdtri.References
- 1
Cephes Mathematical Functions Library, http://www.netlib.org/cephes/