The incomplete Γ function as a continuous poisson distribution

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Abstract

Among the many contributions of Professor Luke to the theory of special functions, the most useful in computational statistics is probably that on the incomplete Γ function. This short paper points out that an incomplete Γ function routine is so important that it should be a standard part of any library of statistical subroutines. The paper goes on to give another example of use of the incomplete Γ function: as a means for computer generation of Poisson random variables. and, having urged wide use of the incomplete Γ function, proceeds with development of a Poisson generator whose principal aim is to avoid use of the very function is has previously lauded. Occasional use of an accurate incomplete Γ routine is essential however, in order that the composite method be exact. © 1986.

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Marsaglia, G. (1986). The incomplete Γ function as a continuous poisson distribution. Computers and Mathematics with Applications, 12(5-6 PART 2), 1187–1190. https://doi.org/10.1016/0898-1221(86)90242-7

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