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 - betaincand \(\Gamma\) is the- gammafunction [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 
 
 - Notes - This function wraps the - ibeta_invroutine 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 - >>> import scipy.special as sc - This function is the inverse of - betaincfor 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