SciPy

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:

dfn : array_like

First parameter (positive float).

dfd : array_like

Second parameter (positive float).

p : array_like

Cumulative probability, in [0, 1].

Returns:

x : 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 [R358] routine fdtri.

References

[R358](1, 2) Cephes Mathematical Functions Library, http://www.netlib.org/cephes/index.html

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