scipy.special.fdtri#

scipy.special.fdtri(dfn, dfd, p, out=None) = <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].

outndarray, optional

Optional output array for the function values

Returns:
xscalar or ndarray

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/