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Lognormal genesis

Published online by Cambridge University Press:  14 July 2016

Gavin Brown  and
J. W. Sanders
Gavin Brown
Affiliation:
The University of New South Wales
J. W. Sanders*
Affiliation:
The University of New South Wales
*
∗Postal address: School of Mathematics, The University of New South Wales, P.O. Box 1, Kensington, NSW 2033, Australia.
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Abstract

Models have been proposed in many diverse areas to generate a lognormal distribution and the underlying idea has always been some form of the law of proportionate effect. In a sense any model must resemble this recipe: take logs and apply the central limit theorem. Our model is no exception. However our formulation is designed to encompass the previous models and demonstrate that the fundamental concept is one of classification. This supersedes a multitude of models which incorporate a mechanism peculiar to a specific application in order to use the law of proportionate effect; we illustrate with applications of the model to ecology, econometrics and geostatistics.

Keywords

LOGNORMAL LAWCLASSIFICATION PROBLEMSINGULAR MEASURESINCOME DISTRIBUTIONECOLOGICAL MODELGEOSTATISTICAL ORE DENSITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 542 - 547
Copyright
Copyright © Applied Probability Trust 

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References

Aitchison, J. and Brown, J. A. C. (1957) The Lognormal Distribution, with Special Reference to its Uses in Economics, Cambridge University Press.Google Scholar
Colinvaux, P. A. (1973) Introduction to Ecology, Wiley, New York.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. 2, Wiley, New York.Google Scholar
Halmos, P. R. (1944) Random alms. Ann. Math. Statist. 15, 182–189.Google Scholar
Kolmogoroff, A. N. (1941) Über das logarithmisch Normale Verteilungsgesetz der Dimensionen der Teilchen bei Zerstückelung, C. R. Acad. Sci. U.R.S.S. 31, 99–101.Google Scholar
Krige, D. G. (1978) Lognormal – de Wijsian Geostatistics for Ore Evaluation, S.A.I.M.M. Series in Geostatistics, No. 1.Google Scholar
Shepp, L. A. (1965) Distinguishing a sequence of random variables from a translate of itself. Ann. Math. Statist. 36, 1107–1112.Google Scholar
Vistelius, A. B. (1967) Studies in Mathematical Geology. Consultants Bureau, New York.Google Scholar