The incomplete Γ function as a continuous poisson distribution

AbstractAmong 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