# 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 [1]

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

Nonnegative real argument

marray_like

Nonnegative real shape parameter

outndarray

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

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 ])