scipy.special.pdtrc#

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

Poisson survival function

Returns the sum of the terms from k+1 to infinity of the Poisson distribution: sum(exp(-m) * m**j / j!, j=k+1..inf) = gammainc( k+1, m). Arguments must both be non-negative doubles.

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 survival function

See also

pdtr: Poisson cumulative distribution function
pdtrik: inverse of pdtr with respect to k
pdtri: inverse of pdtr with respect to m

Notes

pdtrc has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

>>> import numpy as np
>>> import scipy.special as sc

It is a survival function, so it decreases to 0 monotonically as k goes to infinity.

>>> k = np.array([1, 10, 100, np.inf])
>>> sc.pdtrc(k, 1)
array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])

It can be expressed in terms of the lower incomplete gamma function gammainc.

>>> sc.gammainc(k + 1, 1)
array([2.64241118e-001, 1.00477664e-008, 3.94147589e-161, 0.00000000e+000])