Quantile function expansion using regularly varying functions

Thomas Fung*, Eugene Seneta

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We present a simple result that allows us to evaluate the asymptotic order of the remainder of a partial asymptotic expansion of the quantile function h(u) as u → 0+ or 1. This is focussed on important univariate distributions when h(⋅) has no simple closed form, with a view to assessing asymptotic rate of decay to zero of tail dependence in the context of bivariate copulas. Motivation of this study is illustrated by the asymptotic behaviour of the tail dependence of Normal copula. The Normal, Skew-Normal and Gamma are used as initial examples. Finally, we discuss approximation to the lower quantile of the Variance-Gamma and Skew-Slash distributions.

Original languageEnglish
Pages (from-to)1091-1103
Number of pages13
JournalMethodology and Computing in Applied Probability
Volume20
Issue number4
DOIs
Publication statusPublished - 1 Dec 2018

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Keywords

  • Asymptotic expansion
  • Asymptotic tail dependence
  • Quantile function
  • Regularly varying functions
  • Skew-Slash distribution
  • Variance-Gamma distribution

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