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Application of extreme value analysis to Weibull data
Author(s) -
Carter D. J. T.,
Challenor P. G.
Publication year - 1983
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.49710946013
Subject(s) - weibull distribution , extreme value theory , generalized extreme value distribution , mathematics , statistics , exponential distribution , maxima , exponential function , gumbel distribution , distribution fitting , distribution (mathematics) , weibull modulus , population , sample (material) , sample size determination , mathematical analysis , physics , thermodynamics , demography , art , sociology , performance art , art history
In the application of extreme value analysis it is usually assumed that the size of the samples from which the extreme values are obtained is sufficiently large for the asymptotic extreme value distribution to be used. The necessary sample size depends upon the population distribution and this is generally not known; but assuming a Weibull distribution, which is often fitted to wind speed and wave height data, it is shown that the rate of convergence is rapid and that the asymptotic distribution may be used for a sample size as small as ten. An ‘exponential approximation’ for the distribution of maxima is sometimes confused with the extreme value distribution. This approximate form is derived for the Weibull distribution and the essential difference between it and the asymptotic extreme value distribution is explained.