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SECOND ORDER REGULAR VARIATION AND ITS APPLICATIONS TO RATES OF CONVERGENCE IN EXTREME-VALUE DISTRIBUTION
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 Title & Authors
SECOND ORDER REGULAR VARIATION AND ITS APPLICATIONS TO RATES OF CONVERGENCE IN EXTREME-VALUE DISTRIBUTION
Lin, Fuming; Peng, Zuoxiang; Nadarajah, Saralees;
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 Abstract
The rate of convergence of the distribution of order statistics to the corresponding extreme-value distribution may be characterized by the uniform and total variation metrics. de Haan and Resnick [4] derived the convergence rate when the second order generalized regularly varying function has second order derivatives. In this paper, based on the properties of the generalized regular variation and the second order generalized variation and characterized by uniform and total variation metrics, the convergence rates of the distribution of the largest order statistic are obtained under weaker conditions.
 Keywords
second order generalized regularly varying function;extreme value distribution;rate of convergence;total variation metrics;
 Language
English
 Cited by
1.
On the Rate of Convergence of STSD Extremes, Communications in Statistics - Theory and Methods, 2011, 40, 10, 1795  crossref(new windwow)
2.
PROPERTIES OF SECOND-ORDER REGULAR VARIATION AND EXPANSIONS FOR RISK CONCENTRATION, Probability in the Engineering and Informational Sciences, 2012, 26, 04, 535  crossref(new windwow)
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