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 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 ])