Quantile Function Expansion Using Regularly Varying Functions

Thomas Fung () and Eugene Seneta
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Thomas Fung: Macquarie University
Eugene Seneta: University of Sydney

Methodology and Computing in Applied Probability, 2018, vol. 20, issue 4, 1091-1103

Abstract: 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.

Keywords: Asymptotic expansion; Asymptotic tail dependence; Quantile function; Regularly varying functions; Skew-Slash distribution; Variance-Gamma distribution; 60E05; 41A60 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11009-017-9593-0

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