scipy.special.gammaincc#
- scipy.special.gammaincc(a, x, out=None) = <ufunc 'gammaincc'>#
- Regularized upper incomplete gamma function. - It is defined as \[Q(a, x) = \frac{1}{\Gamma(a)} \int_x^\infty t^{a - 1}e^{-t} dt\]- for \(a > 0\) and \(x \geq 0\). See [dlmf] for details. - Parameters:
- aarray_like
- Positive parameter 
- xarray_like
- Nonnegative argument 
- outndarray, optional
- Optional output array for the function values 
 
- Returns:
- scalar or ndarray
- Values of the upper incomplete gamma function 
 
 - See also - gammainc
- regularized lower incomplete gamma function 
- gammaincinv
- inverse of the regularized lower incomplete gamma function 
- gammainccinv
- inverse of the regularized upper incomplete gamma function 
 - Notes - The function satisfies the relation - gammainc(a, x) + gammaincc(a, x) = 1where- gammaincis the regularized lower incomplete gamma function.- The implementation largely follows that of [boost]. - References [dlmf]- NIST Digital Library of Mathematical functions https://dlmf.nist.gov/8.2#E4 [boost]- Maddock et. al., “Incomplete Gamma Functions”, https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html - Examples - >>> import scipy.special as sc - It is the survival function of the gamma distribution, so it starts at 1 and monotonically decreases to 0. - >>> sc.gammaincc(0.5, [0, 1, 10, 100, 1000]) array([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45, 0.00000000e+00]) - It is equal to one minus the lower incomplete gamma function. - >>> a, x = 0.5, 0.4 >>> sc.gammaincc(a, x) 0.37109336952269756 >>> 1 - sc.gammainc(a, x) 0.37109336952269756