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A transformation for normal extremes

Published online by Cambridge University Press:  14 July 2016

H. E. Daniels
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Abstract

A transformation is introduced to stabilize the variance of the largest value in a sample from a normal distribution. The transformed distribution is found to approximate closely to the limiting Gumbel form for all sample sizes. The practical implications of the result are discussed.

Keywords

EXTREME VALUESTRANSFORMATIONSGUMBEL DISTRIBUTION

Information

Type
Part 5 — Statistical Theory
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 201 - 206
Copyright
Copyright © 1982 Applied Probability Trust 

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References

[1] Daniels, H. E. (1941) A property of the distribution of extremes. Biometrika 32, 194–195.Google Scholar
[2] Fisher, R. A. and Tippett, L. H. C. (1928) Limiting forms of the frequency distribution of the largest or smallest member of a sample. Proc. Camb. Phil. Soc. 24, 180–190.CrossRefGoogle Scholar
[3] Gumbel, E. J. (1958) Statistics of Extremes. Columbia University Press, New York.Google Scholar