scipy.special.btdtrib#

scipy.special.btdtrib(a, p, x, out=None) = <wrapped_ufunc 'btdtrib'>#

Inverse of betainc with respect to b.

This is the inverse of the beta cumulative distribution function, betainc, considered as a function of b, returning the value of b for which betainc(a, b, x) = p, or

\[p = \int_0^x \frac{\Gamma(a + b)}{\Gamma(a)\Gamma(b)} t^{a-1} (1-t)^{b-1}\,dt\]

Parameters:

aarray_like: Shape parameter (a > 0).
parray_like: Cumulative probability, in [0, 1].
xarray_like: The quantile, in [0, 1].
outndarray, optional: Optional output array for the function values

Returns:

bscalar or ndarray: The value of the shape parameter b such that betainc(a, b, x) = p.

See also

betainc: Regularized incomplete beta function
betaincinv: Inverse of the regularized incomplete beta function with respect to x.
btdtria: Inverse of the beta cumulative distribution function, with respect to a.

Notes

Wrapper for the ibeta_invb routine from the Boost Math C++ library [1].

Array API Standard Support

btdtrib 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. btdtrib does not currently support out for the PyTorch backend.

See Support for the array API standard for more information.

References

[1]

The Boost Developers. “Boost C++ Libraries”. https://www.boost.org/.

Examples

>>> import scipy.special as sc
>>> a, b, x = 1.2, 3.1, 0.2
>>> y = sc.betainc(a, b, x)

btdtrib is the inverse of betainc for fixed values of \(a\) and \(x\):

>>> sc.btdtrib(a, y, x)
3.1