Module « scipy.special »

Fonction pdtr - module scipy.special

Signature de la fonction pdtr

Description

pdtr.__doc__

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

pdtr(k, m, out=None)

Poisson cumulative distribution function.

Defined as the probability that a Poisson-distributed random
variable with event rate :math:`m` is less than or equal to
:math:`k`. More concretely, this works out to be [1]_

.. math::

   \exp(-m) \sum_{j = 0}^{\lfloor{k}\rfloor} \frac{m^j}{m!}.

Parameters
----------
k : array_like
    Nonnegative real argument
m : array_like
    Nonnegative real shape parameter
out : ndarray
    Optional output array for the function results

See Also
--------
pdtrc : Poisson survival function
pdtrik : inverse of `pdtr` with respect to `k`
pdtri : inverse of `pdtr` with respect to `m`

Returns
-------
scalar or ndarray
    Values of the Poisson cumulative distribution function

References
----------
.. [1] https://en.wikipedia.org/wiki/Poisson_distribution

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

It is a cumulative distribution function, so it converges to 1
monotonically as `k` goes to infinity.

>>> sc.pdtr([1, 10, 100, np.inf], 1)
array([0.73575888, 0.99999999, 1.        , 1.        ])

It is discontinuous at integers and constant between integers.

>>> sc.pdtr([1, 1.5, 1.9, 2], 1)
array([0.73575888, 0.73575888, 0.73575888, 0.9196986 ])