We present a simple result that allows us to evaluate the asymptotic order ofthe remainder of a partial asymptotic expansion of the quantile function $h(u)$as $u\to 0^+$ or $1^-$. This is focussed on important univariate distributionswhen $h(\cdot)$ has no simple closed form, with a view to assessing asymptoticrate of decay to zero of tail dependence in the context of bivariate copulas.The Introduction motivates the study in terms of the standard Normal. TheNormal, Skew-Normal and Gamma are used as initial examples. Finally, we discussapproximation to the lower quantile of the Variance-Gamma and Skew-Slashdistributions.
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