# Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios

@article{Gil2012EfficientAA, title={Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios}, author={Amparo Gil and J. Segura and N. Temme}, journal={SIAM J. Sci. Comput.}, year={2012}, volume={34} }

Algorithms for the numerical evaluation of the incomplete gamma function ratios $P(a,x)=\gamma(a,x)/\Gamma(a)$ and $Q(a,x)=\Gamma(a,x)/\Gamma(a)$ are described for positive values of $a$ and $x$. Also, inversion methods are given for solving the equations $P(a,x)=p$, $Q(a,x)=q$, with $0<p,q<1$. Both the direct computation and the inversion of the incomplete gamma function ratios are used in many problems in statistics and applied probability. The analytical approach from earlier literature is… Expand

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