scipy.special.bdtrc

scipy.special.bdtrc(k, n, p, out=None) = <ufunc 'bdtrc'>

Binomial distribution survival function.

Sum of the terms floor(k) + 1 through n of the binomial probability density,

\[\mathrm{bdtrc}(k, n, p) = \sum_{j=\lfloor k \rfloor +1}^n {{n}\choose{j}} p^j (1-p)^{n-j}\]

Parameters:

karray_like

Number of successes (double), rounded down to nearest integer.

narray_like

Number of events (int)

parray_like

Probability of success in a single event.

outndarray, optional

Optional output array for the function values

Returns:

yscalar or ndarray

Probability of floor(k) + 1 or more successes in n independent events with success probabilities of p.

See also

bdtr

betainc

Notes

The terms are not summed directly; instead the regularized incomplete beta function is employed, according to the formula,

\[\mathrm{bdtrc}(k, n, p) = I_{p}(\lfloor k \rfloor + 1, n - \lfloor k \rfloor).\]

Wrapper for the Cephes [1] routine bdtrc.

bdtrc 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.

References

[1]

Cephes Mathematical Functions Library, http://www.netlib.org/cephes/