scipy.special.betaincinv#

scipy.special.betaincinv(a, b, y, out=None) = <ufunc 'betaincinv'>#

Inverse of the regularized incomplete beta function.

Computes \(x\) such that:

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

where \(I_x\) is the normalized incomplete beta function betainc and \(\Gamma\) is the gamma function [1].

Parameters:

a, barray_like: Positive, real-valued parameters
yarray_like: Real-valued input
outndarray, optional: Optional output array for function values

Returns:

scalar or ndarray: Value of the inverse of the regularized incomplete beta function

See also

betainc: regularized incomplete beta function
gamma: gamma function

Notes

This function wraps the ibeta_inv routine from the Boost Math C++ library [2].

betaincinv 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]

NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/8.17

[2]

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

Examples

>>> import scipy.special as sc

This function is the inverse of betainc for fixed values of \(a\) and \(b\).

>>> a, b = 1.2, 3.1
>>> y = sc.betainc(a, b, 0.2)
>>> sc.betaincinv(a, b, y)
0.2
>>>
>>> a, b = 7.5, 0.4
>>> x = sc.betaincinv(a, b, 0.5)
>>> sc.betainc(a, b, x)
0.5