Quantile function expansion using regularly varying functions

Thomas Fung, Eugene Seneta

Research output: Contribution to journalArticleResearchpeer-review

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.

LanguageEnglish
Pages1091-1103
Number of pages13
JournalMethodology and Computing in Applied Probability
Volume20
Issue number4
DOIs
Publication statusPublished - 1 Dec 2018

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Regularly Varying Function
Tail Dependence
Quantile Function
Copula
Skew
Quantile
Remainder
Univariate
Asymptotic Expansion
Closed-form
Asymptotic Behavior
Decay
Partial
Evaluate
Zero
Approximation
Context

Cite this

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Quantile function expansion using regularly varying functions. / Fung, Thomas; Seneta, Eugene.

In: Methodology and Computing in Applied Probability, Vol. 20, No. 4, 01.12.2018, p. 1091-1103.

Research output: Contribution to journalArticleResearchpeer-review

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