Abstract
Methods for determining from a set of data the type of the extreme value distribution that attracts the population distribution are developed. The methods are based on the fact that the cumulative distribution functions of the three classical types for the maximum, when drawn on a Gumbel probability paper, exhibit different curvatures. Both a quick “visual selection method” and a more accurate “fit of attraction test” are discussed. The test statistics are location and scale invariant. The asymptotic results leading to the tests are of independent interest. In order to make our proposed test applicable for small sample sizes, the distribution of our major test statistic is tabulated for Gumbel, uniform, exponential and Cauchy parents via Monte Carlo simulation. Finally, our methods are demonstrated by reevaluating a published set of data.
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© 1989 Springer-Verlag Berlin Heidelberg
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Castillo, E., Galambos, J., Sarabia, J.M. (1989). The Selection of the Domain of Attraction of an Extreme Value Distribution from a Set of Data. In: Hüsler, J., Reiss, RD. (eds) Extreme Value Theory. Lecture Notes in Statistics, vol 51. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3634-4_16
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DOI: https://doi.org/10.1007/978-1-4612-3634-4_16
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-96954-1
Online ISBN: 978-1-4612-3634-4
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