scipy.special.btdtria#

scipy.special.btdtria(p, b, x, out=None) = <ufunc 'btdtria'>#

Inverse of betainc with respect to a.

This is the inverse of the beta cumulative distribution function, betainc, considered as a function of a, returning the value of a 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:

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

Returns:

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

See also

betainc: Regularized incomplete beta function
betaincinv: Inverse of the regularized incomplete beta function
btdtrib: Inverse of the beta cumulative distribution function, with respect to b.

Notes

This function wraps the ibeta_inva 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

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

>>> a, b, x = 1.2, 3.1, 0.2
>>> y = sc.betainc(a, b, x)
>>> sc.btdtria(y, b, x)
1.2