scipy.special.betaincc#
- scipy.special.betaincc(a, b, x, out=None) = <ufunc 'betaincc'>#
- Complement of the regularized incomplete beta function. - Computes the complement of the regularized incomplete beta function, defined as [1]: \[\bar{I}_x(a, b) = 1 - I_x(a, b) = 1 - \frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)} \int_0^x t^{a-1}(1-t)^{b-1}dt,\]- for \(0 \leq x \leq 1\). - Parameters:
- a, barray_like
- Positive, real-valued parameters 
- xarray_like
- Real-valued such that \(0 \leq x \leq 1\), the upper limit of integration 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- scalar or ndarray
- Value of the regularized incomplete beta function 
 
 - See also - betainc
- regularized incomplete beta function 
- betaincinv
- inverse of the regularized incomplete beta function 
- betainccinv
- inverse of the complement of the regularized incomplete beta function 
- beta
- beta function 
- scipy.stats.beta
- beta distribution 
 - Notes - Added in version 1.11.0. - This function wraps the - ibetacroutine from the Boost Math C++ library [2].- 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 - >>> from scipy.special import betaincc, betainc - The naive calculation - 1 - betainc(a, b, x)loses precision when the values of- betainc(a, b, x)are close to 1:- >>> 1 - betainc(0.5, 8, [0.9, 0.99, 0.999]) array([2.0574632e-09, 0.0000000e+00, 0.0000000e+00]) - By using - betaincc, we get the correct values:- >>> betaincc(0.5, 8, [0.9, 0.99, 0.999]) array([2.05746321e-09, 1.97259354e-17, 1.96467954e-25])