Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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SECOND ORDER REGULAR VARIATION AND ITS APPLICATIONS TO RATES OF CONVERGENCE IN EXTREME-VALUE DISTRIBUTION

  • Lin, Fuming (DEPARTMENT OF MATHEMATICS SICHUAN UNIVERSITY OF SCIENCES & ENGINEERING) ;
  • Peng, Zuoxiang (SCHOOL OF MATHEMATICS AND STATISTICS SOUTHWEST UNIVERSITY) ;
  • Nadarajah, Saralees (SCHOOL OF MATHEMATICS UNIVERSITY OF MANCHESTER)
  • Published : 2008.02.29
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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.

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References

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Cited by

  1. On the Rate of Convergence of STSD Extremes vol.40, pp.10, 2011, https://doi.org/10.1080/03610921003695726
  2. PROPERTIES OF SECOND-ORDER REGULAR VARIATION AND EXPANSIONS FOR RISK CONCENTRATION vol.26, pp.04, 2012, https://doi.org/10.1017/S0269964812000174