Quantile function expansion using regularly varying functions

Thomas Fung*, Eugene Seneta

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    3 Citations (Scopus)


    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
    Issue number4
    Publication statusPublished - 1 Dec 2018


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


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