# scipy.special.pdtr#

scipy.special.pdtr(k, m, out=None) = <ufunc 'pdtr'>#

Poisson cumulative distribution function.

Defined as the probability that a Poisson-distributed random variable with event rate $$m$$ is less than or equal to $$k$$. More concretely, this works out to be 

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

Number of occurrences (nonnegative, real)

marray_like

Shape parameter (nonnegative, real)

outndarray, optional

Optional output array for the function results

Returns:
scalar or ndarray

Values of the Poisson cumulative distribution function

pdtrc

Poisson survival function

pdtrik

inverse of pdtr with respect to k

pdtri

inverse of pdtr with respect to m

References

Examples

>>> import numpy as np
>>> 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 ])