Module « scipy.special »

Fonction fdtri - module scipy.special

Signature de la fonction fdtri

Description

fdtri.__doc__

fdtri(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

fdtri(dfn, dfd, p)

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, :math:`I^{-1}_x(a, b)`.  Let
:math:`z = I^{-1}_p(d_d/2, d_n/2).`  Then,

.. math::
    x = \frac{d_d (1 - z)}{d_n z}.

If `p` is such that :math:`x < 0.5`, the following relation is used
instead for improved stability: let
:math:`z' = I^{-1}_{1 - p}(d_n/2, d_d/2).` Then,

.. math::
    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/