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The Saddlepoint Approximation for a General Birth Process

H. E. Daniels
Journal of Applied Probability
Vol. 19, No. 1 (Mar., 1982), pp. 20-28
DOI: 10.2307/3213912
Stable URL: http://www.jstor.org/stable/3213912
Page Count: 9
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Saddlepoint Approximation for a General Birth Process
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Abstract

Saddlepoint approximations to the probabilities for a general time-homogeneous birth process are derived from the known Laplace transform with respect to time. Numerical computations for the simple (logistic) epidemic show the approximation to have a remarkably low relative error over the useful range of times for populations as small as 5. The merit or otherwise of renormalising the approximate probabilities is discussed. To study the accuracy for moderately large population sizes, a special form of birth rate is used, for which the exact probabilities can be computed directly.

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