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Bounds for moment generating functions and for extinction probabilities

Published online by Cambridge University Press:  14 July 2016

D. Brook
D. Brook*
Affiliation:
University of Manchester
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Extract

Suppose that we have a non-negative, real valued random variable x, whose distribution is governed by some unknown moment generating function M(t). Suppose further that we are given certain moments of x, then the question to be discussed in this paper is : can we find a sharp upper bounding function for the m.g.f.? It will be shown that this is usually possible both in the single variate case and in its natural extension to the multivariate case.

Type
Research Papers
Information
Journal of Applied Probability , Volume 3 , Issue 1 , June 1966 , pp. 171 - 178
Copyright
Copyright © Sheffield: Applied Probability Trust 

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References

Harris, T. E. (1963) The Theory of Branching Processes. Springer-Verlag.Google Scholar
Isii, K. (1959) On a method for generalisation of Tchebycheff's inequality. Ann. Inst. Statist. Math. Tokyo, 10, 65–88.CrossRefGoogle Scholar
Kingman, J. F. C. (1963) On inequalities of the Tchebychev type. Proc. Camb. Phil. Soc. 59, 135–146.Google Scholar