On fractional linear bounds for probability generating functions
- 1 December 1986
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 23 (4) , 904-913
- https://doi.org/10.2307/3214464
Abstract
The best upper and lower bounds for any probability generating function with mean m and finite variance are derived within the family of fractional linear functions with mean m. These are often intractable and simpler bounds, more useful for practical purposes, are then constructed. Direct applications in branching and epidemic theories are briefly presented; a slight improvement of the bounds is obtained for infinitely divisible distributions.Keywords
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