The Regularized Incomplete Gamma Q function is defined as:
\[
Q(s,x)=\frac{\Gamma(s,x)}{\Gamma(s)}=1-P(s,x), s \geq 0, x \geq 0
\]
The algorithm used for computing the regularized incomplete Gamma Q function depends on the values of
s and
x.
- For \(s > 100\), Q is approximated using the Gauss-Legendre quadrature.
- For \(x < s + 1\), Q is approximated using the Pearson's series representation.
- Otherwise, Q is approximated using the continued fraction expression by Legendre.
The R equivalent function is
pgamma. E.g.,
pgamma(x, s, lower=FALSE).