Module « scipy.special »

Fonction betaincinv - module scipy.special

Signature de la fonction betaincinv

Description

betaincinv.__doc__

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

betaincinv(a, b, y, out=None)

Inverse of the incomplete beta function.

Computes :math:`x` such that:

.. math::

    y = I_x(a, b) = \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}
    \int_0^x t^{a-1}(1-t)^{b-1}dt,

where :math:`I_x` is the normalized incomplete beta
function `betainc` and
:math:`\Gamma` is the `gamma` function [1]_.

Parameters
----------
a, b : array-like
    Positive, real-valued parameters
y : array-like
    Real-valued input
out : ndarray, optional
    Optional output array for function values

Returns
-------
array-like
    Value of the inverse of the incomplete beta function

See Also
--------
betainc : incomplete beta function
gamma : gamma function

References
----------
.. [1] NIST Digital Library of Mathematical Functions
       https://dlmf.nist.gov/8.17

Examples
--------
>>> import scipy.special as sc

This function is the inverse of `betainc` for fixed
values of :math:`a` and :math:`b`.

>>> a, b = 1.2, 3.1
>>> y = sc.betainc(a, b, 0.2)
>>> sc.betaincinv(a, b, y)
0.2
>>>
>>> a, b = 7.5, 0.4
>>> x = sc.betaincinv(a, b, 0.5)
>>> sc.betainc(a, b, x)
0.5