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# 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:
    k array_like

      Number of occurrences (nonnegative, real)

    m array_like

      Shape parameter (nonnegative, real)

    out ndarray, 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 | ✅ | ⛔
  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])