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The saddlepoint approximation for a general birth process

Published online by Cambridge University Press:  14 July 2016

H. E. Daniels
H. E. Daniels*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge, CB2 1SB, U.K.
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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.

Keywords

BIRTH PROCESSSIMPLE EPIDEMICSADDLEPOINT APPROXIMATION
Type
Research Paper
Information
Journal of Applied Probability , Volume 19 , Issue 1 , March 1982 , pp. 20 - 28
Copyright
Copyright © Applied Probability Trust 1982 

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