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

Author

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  • Gordon K. Smyth

    (University of Queensland)

  • Heather M. Podlich

    (University of Queensland)

Abstract

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 reordered into a linear increasing sequence.

Suggested Citation

  • Gordon K. Smyth & Heather M. Podlich, 2002. "An Improved Saddlepoint Approximation Based on the Negative Binomial Distribution for the General Birth Process," Computational Statistics, Springer, vol. 17(1), pages 17-28, March.
    • Handle: RePEc:spr:compst:v:17:y:2002:i:1:d:10.1007_s001800200088
    DOI: 10.1007/s001800200088
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    Cited by:

    1. M. J. Faddy & D. M. Smith, 2008. "Extended Poisson process modelling of dilution series data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 461-471, September.

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