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