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 support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	✅	⛔
Dask	✅	n/a

For the NumPy backend, this function supports all NumPy ufunc keyword arguments. Other backends may support out, but none of the other ufunc kwargs. out is typically supported for CuPy and PyTorch, but not currently in cases where SciPy relies on a generic Array API implementation or, for PyTorch on CPU, falls back to the NumPy backend. out is never supported for JAX because JAX arrays are immutable. pdtrc does not currently support out for the PyTorch backend.

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])