Module « scipy.special »

Fonction btdtria - module scipy.special

Signature de la fonction btdtria

Description

btdtria.__doc__

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

btdtria(p, b, x)

Inverse of `btdtr` with respect to `a`.

This is the inverse of the beta cumulative distribution function, `btdtr`,
considered as a function of `a`, returning the value of `a` for which
`btdtr(a, b, x) = p`, or

.. math::
    p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt

Parameters
----------
p : array_like
    Cumulative probability, in [0, 1].
b : array_like
    Shape parameter (`b` > 0).
x : array_like
    The quantile, in [0, 1].

Returns
-------
a : ndarray
    The value of the shape parameter `a` such that `btdtr(a, b, x) = p`.

See Also
--------
btdtr : Cumulative distribution function of the beta distribution.
btdtri : Inverse with respect to `x`.
btdtrib : Inverse with respect to `b`.

Notes
-----
Wrapper for the CDFLIB [1]_ Fortran routine `cdfbet`.

The cumulative distribution function `p` is computed using a routine by
DiDinato and Morris [2]_. Computation of `a` involves a search for a value
that produces the desired value of `p`. The search relies on the
monotonicity of `p` with `a`.

References
----------
.. [1] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.
.. [2] DiDinato, A. R. and Morris, A. H.,
       Algorithm 708: Significant Digit Computation of the Incomplete Beta
       Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373.