scipy.special.btdtrib#

scipy.special.btdtrib(a, p, x, out=None) = <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].

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