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

Array API Standard Support

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])