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A simple construction of an upper bound for the mean of the maximum of n identically distributed random variables

Published online by Cambridge University Press:  14 July 2016

A. Gravey
A. Gravey*
Affiliation:
Centre National d'Etudes des Télécommunications
*
∗ Postal address: CNET, BP 40, 22301 Lannion Cedex, France.
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Abstract

This note gives a method of finding an upper bound for the mean of the maximum of n identically distributed non-negative random variables. The bound is explicitly given and numerically compared with the exact value of the mean of the maximum for some classical distributions (geometric, Poisson, Erlang, hyperexponential).

Keywords

ORDER STATISTICSGEOMETRIC DISTRIBUTIONPOISSON DISTRIBUTIONERLANG DISTRIBUTIONHYPEREXPONENTIAL DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 844 - 851
Copyright
Copyright © Applied Probability Trust 1985 

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References

David, H. A. (1972) Order Statistics. Wiley, New York.Google Scholar
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