Computational Statistics

, Volume 17, Issue 1, pp 17–28 | Cite as

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

  • Gordon K. Smyth
  • Heather M. Podlich


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 reordered into a linear increasing sequence.


saddlepoint approximation birth process negative binomial distribution binomial distribution exponential tilting 



Much of the work leading to this paper was completed while the first author was a visiting Associate Professor at the University of Southern Denmark.


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Copyright information

© Physica-Verlag 2002

Authors and Affiliations

  • Gordon K. Smyth
    • 1
  • Heather M. Podlich
    • 1
  1. 1.Department of Mathematics and School of Land and FoodUniversity of QueenslandBrisbaneAustralia

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