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
New in version 1.11.0.
References
[1]NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/8.17
Examples
>>> from scipy.special import betaincc, betainc
The naive calculation
1 - betainc(a, b, x)
loses precision when the values ofbetainc(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])