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/