= Cornish-Fisher expansion
{c}
{title2=$y_\alpha=z_\alpha+\gamma_1(z_\alpha^2-1)/(6\sqrt n)+O(n^{-1})$}
{wiki}
The Cornish-Fisher expansion inverts an <Edgeworth expansion> to approximate <quantiles>. For a standardized iid sum, let $\gamma_1$ be the <skewness> of one summand and $z_\alpha$ the <standard normal quantile>. The first <distribution function> correction is $-\gamma_1(z^2-1)\phi(z)/(6\sqrt n)$. Substituting $y_\alpha=z_\alpha+c/\sqrt n$ and expanding $\Phi$ gives $c=\gamma_1(z_\alpha^2-1)/6$. This is a fixed-quantile asymptotic, with $\alpha$ fixed in $(0,1)$.
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