Module « scipy.special »

Fonction bdtr - module scipy.special

Signature de la fonction bdtr

Description

bdtr.__doc__

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

bdtr(k, n, p)

Binomial distribution cumulative distribution function.

Sum of the terms 0 through `floor(k)` of the Binomial probability density.

.. math::
    \mathrm{bdtr}(k, n, p) = \sum_{j=0}^{\lfloor k \rfloor} {{n}\choose{j}} p^j (1-p)^{n-j}

Parameters
----------
k : array_like
    Number of successes (double), rounded down to the nearest integer.
n : array_like
    Number of events (int).
p : array_like
    Probability of success in a single event (float).

Returns
-------
y : ndarray
    Probability of `floor(k)` or fewer successes in `n` independent events with
    success probabilities of `p`.

Notes
-----
The terms are not summed directly; instead the regularized incomplete beta
function is employed, according to the formula,

.. math::
    \mathrm{bdtr}(k, n, p) = I_{1 - p}(n - \lfloor k \rfloor, \lfloor k \rfloor + 1).

Wrapper for the Cephes [1]_ routine `bdtr`.

References
----------
.. [1] Cephes Mathematical Functions Library,
       http://www.netlib.org/cephes/