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An expansion for the distribution function of a random sum

Published online by Cambridge University Press:  14 July 2016

L. M. Marsh
L. M. Marsh*
Affiliation:
James Cook University of North Queensland
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Abstract

The Edgeworth expansion gives an indication of the rate of convergence of the distribution function of the sum of a fixed number of random variables to the normal distribution. A similar expansion is given here for the distribution function of the sum of a random number N of random variables, when the probability generating function of N takes a special form.

Keywords

RANDOM SUMEDGEWORTH EXPANSIONRATE OF CONVERGENCECENTRAL LIMIT THEOREM
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 869 - 874
Copyright
Copyright © Applied Probability Trust 1973 

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References

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