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1 results

  • Samples with a limit shape, multivariate extremes, and risk

  • Part of
  • Guus Balkema, Natalia Nolde
  • Journal:
    Advances in Applied Probability / Volume 52 / Issue 2 / June 2020
    Published online by Cambridge University Press:
    15 July 2020, pp. 491-522
    Print publication:
    June 2020

  • Large samples from a light-tailed distribution often have a well-defined shape. This paper examines the implications of the assumption that there is a limit shape. We show that the limit shape determines the upper quantiles for a large class of random variables. These variables may be described loosely as continuous homogeneous functionals of the underlying random vector. They play an important role in evaluating risk in a multivariate setting. The paper also looks at various coefficients of tail dependence and at the distribution of the scaled sample points for large samples. The paper assumes convergence in probability rather than almost sure convergence. This results in an elegant theory. In particular, there is a simple characterization of domains of attraction.