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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
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3213912
Page Count: 9
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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.
Journal of Applied Probability © 1982 Applied Probability Trust