Algorithm 955: approximation of the inverse Poisson cumulative distribution function. New approximations for the inverse of the incomplete gamma function are derived, which are used to develop efficient evaluations of the inverse Poisson cumulative distribution function. An asymptotic approximation based on the standard Normal approximation is particularly good for CPUs with MIMD cores, while for GPUs and other hardware with vector units, a second asymptotic approximation based on Temme’s approximation of the incomplete gamma function is more efficient due to conditional branching within each vector. The accuracy and efficiency of the software implementations is assessed on both CPUs and GPUs.

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