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On fractional linear bounds for probability generating functions

Published online by Cambridge University Press:  24 August 2016

Claude Lefevre ,
Marc Hallin  and
Prakash Narayan
Claude Lefevre*
Affiliation:
Université Libre de Bruxelles
Marc Hallin*
Affiliation:
Université Libre de Bruxelles
Prakash Narayan
Affiliation:
Monash University
*
∗Postal address: Université Libre de Bruxelles, Institut de Statistique, Campus Plaine, C.P.210, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
∗Postal address: Université Libre de Bruxelles, Institut de Statistique, Campus Plaine, C.P.210, Boulevard du Triomphe, B-1050 Bruxelles, Belgium.
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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

FRACTIONAL LINEAR FUNCTIONINFINITELY DIVISIBLE DISTRIBUTIONBOUNDSBRANCHING PROCESSS–I–S INFECTIOUS DISEASE
Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 4 , December 1986 , pp. 904 - 913
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

∗∗

Present address: American Health and Life Insurance Company, 300 St Paul Place, BSP 14B, Baltimore, MD 21202, USA.

References

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