Using the equation following (5.26), show by reversal of series, that X may be expressed as the following polynomial in the normally distributed random variable Y X = Y + ρ3 (Y 2 − 1)/6 + ρ4 (Y 3 − 3Y )/24 − ρ

2 3 (2Y 3 − 5Y )/36 Hence, express the approximate percentage points of X in terms of standard normal percentage points (Cornish & Fisher, 1937).