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: 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

See also

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 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 ])