scipy.special.owens_t#

scipy.special.owens_t(h, a, out=None) = <wrapped_ufunc 'owens_t'>#

Owen’s T Function.

The function T(h, a) gives the probability of the event (X > h and 0 < Y < a * X) where X and Y are independent standard normal random variables.

Parameters:

harray_like: Input value.
aarray_like: Input value.
outndarray, optional: Optional output array for the function results

Returns:

t: scalar or ndarray: Probability of the event (X > h and 0 < Y < a * X), where X and Y are independent standard normal random variables.

Notes

Array API Standard Support

owens_t 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 typically 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. owens_t does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

References

[1]

M. Patefield and D. Tandy, “Fast and accurate calculation of Owen’s T Function”, Statistical Software vol. 5, pp. 1-25, 2000.

Examples

>>> from scipy import special
>>> a = 3.5
>>> h = 0.78
>>> special.owens_t(h, a)
0.10877216734852274