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Attainable bounds for expectations

Part of: Markov processes Distribution theory - Probability

Published online by Cambridge University Press:  09 April 2009

E. Seneta  and
N. C. Weber
E. Seneta
Affiliation:
Department of Mathematical Statistics The University of SydneyN.S.W. 2006, Australia
N. C. Weber
Affiliation:
Department of Mathematical Statistics The University of SydneyN.S.W. 2006, Australia
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Abstract

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A simple technique for obtaining bounds in terms of means and variances for the expectations of certain functions of random variables in a given class is examined. The bounds given are sharp in the sense that they are attainable by at least one random variable in the class. This technique is applied to obtain bounds for moment generating functions, the coefficient of skewness and parameters associated with branching processes. In particular an improved lower bound for the Malthusian parameter in an age-dependent branching process is derived.

MSC classification

Secondary: 60E15: Inequalities; stochastic orderings 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 3 , December 1982 , pp. 411 - 420
Copyright
Copyright © Australian Mathematical Society 1982

References

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