Module « scipy.special »

Fonction nbdtrik - module scipy.special

Signature de la fonction nbdtrik

Description

nbdtrik.__doc__

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

nbdtrik(y, n, p)

Inverse of `nbdtr` vs `k`.

Returns the inverse with respect to the parameter `k` of
`y = nbdtr(k, n, p)`, the negative binomial cumulative distribution
function.

Parameters
----------
y : array_like
    The probability of `k` or fewer failures before `n` successes (float).
n : array_like
    The target number of successes (positive int).
p : array_like
    Probability of success in a single event (float).

Returns
-------
k : ndarray
    The maximum number of allowed failures such that `nbdtr(k, n, p) = y`.

See also
--------
nbdtr : Cumulative distribution function of the negative binomial.
nbdtri : Inverse with respect to `p` of `nbdtr(k, n, p)`.
nbdtrin : Inverse with respect to `n` of `nbdtr(k, n, p)`.

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

Formula 26.5.26 of [2]_,

.. math::
    \sum_{j=k + 1}^\infty {{n + j - 1}\choose{j}} p^n (1 - p)^j = I_{1 - p}(k + 1, n),

is used to reduce calculation of the cumulative distribution function to
that of a regularized incomplete beta :math:`I`.

Computation of `k` involves a search for a value that produces the desired
value of `y`.  The search relies on the monotonicity of `y` with `k`.

References
----------
.. [1] Barry Brown, James Lovato, and Kathy Russell,
       CDFLIB: Library of Fortran Routines for Cumulative Distribution
       Functions, Inverses, and Other Parameters.
.. [2] Milton Abramowitz and Irene A. Stegun, eds.
       Handbook of Mathematical Functions with Formulas,
       Graphs, and Mathematical Tables. New York: Dover, 1972.