scipy.special.gammainc#
- scipy.special.gammainc(a, x, out=None) = <ufunc 'gammainc'>#
- Regularized lower incomplete gamma function. - It is defined as \[P(a, x) = \frac{1}{\Gamma(a)} \int_0^x t^{a - 1}e^{-t} dt\]- 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 lower incomplete gamma function 
 
 - See also - gammaincc
- regularized upper 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- gammainccis the regularized upper 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 CDF of the gamma distribution, so it starts at 0 and monotonically increases to 1. - >>> sc.gammainc(0.5, [0, 1, 10, 100]) array([0. , 0.84270079, 0.99999226, 1. ]) - It is equal to one minus the upper incomplete gamma function. - >>> a, x = 0.5, 0.4 >>> sc.gammainc(a, x) 0.6289066304773024 >>> 1 - sc.gammaincc(a, x) 0.6289066304773024