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Summary Daniels (JAP 1982) gave a saddlepoint approximation to the probabilities of a general birth process. This paper gives an improved approximation which is only slightly more complex than Daniels' approximation and which has considerably reduced relative error in most cases. The new approximation has the characteristic that it is exact whenever the birth rates can be re- ordered into a linear increasing sequence.

An Improved Saddlepoint Approximation Based on the Negative Binomial Distribution for the General Birth Process