Quantile function expansion using regularly varying functions

2017/05/26 by Thomas Fung, E. Seneta, Fung, Thomas +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #41A60 #60E05 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability and Risk Models #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1705.09494

openalex publication_date 2017/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. The Introduction motivates the study in terms of the standard Normal. 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.

Related

• Convergence rate to a lower tail dependence coefficient of a skew-t distribution
• A New Approximation to the Normal Distribution Quantile Function
• Tail dependence convergence rate for the bivariate skew normal under the equal-skewness condition
• Quantile Mechanics 3: Series Representations and Approximation of some\n Quantile Functions appearing in Finance
• A quantile-based bivariate distribution