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Continuous majorisation and randomness

Published online by Cambridge University Press:  14 July 2016

Raymond J. Hickey
Raymond J. Hickey*
Affiliation:
New University of Ulster
*
∗Postal address: Department of Mathematics, New University of Ulster, Coleraine, Co. Londonderry, BT52 1SA, Northern Ireland.
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Abstract

Majorisation is used to compare continuous distributions in terms of randomness. General results on randomness in the continuous case are given and these are used to investigate the connection between randomness and parameter values in some well-known families of distributions including the normal and gamma.

Keywords

CONVOLUTIONSUNCERTAINTY PARAMETER
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 924 - 929
Copyright
Copyright © Applied Probability Trust 1984 

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References

Hardy, G. H., Littlewood, J. E. and Pólya, G. (1929) Some simple inequalities satisfied by convex functions. Messenger of Math. 58, 45–52.Google Scholar
Hickey, R. J. (1982) A note on the measurement of randomness. J. Appl. Prob. 19, 229–232.Google Scholar
Hickey, R. J. (1983) Majorisation, randomness and some discrete distributions. J. Appl. Prob. 20, 897–902.Google Scholar
Marshall, A. W. and Olkin, I. (1979) Inequalities: The Theory of Majorisation and its Applications. Academic Press, New York.Google Scholar
Renyi, A. (1970) Probability Theory. North-Holland, Amsterdam.Google Scholar
Reza, F. M. (1961) An Introduction to Information Theory. McGraw-Hill, New York.Google Scholar
Ryff, J. V. (1963) On the representation of doubly stochastic operators. Pacific J. Math. 13, 1379–1386.Google Scholar
Shannon, C. E. and Weaver, W. (1964) The Mathematical Theory of Communication. University of Illinois Press, Urbana.Google Scholar