# Cornish Fisher VaR Parameters Calibration

I am trying to calculate Cornish-Fisher (modified VaR), but I am in a trouble because when I am reading some articles, some authors calculate the Cornish-Fisher expansion taking parameters S and K, as the skewness and excess kurtosis of observed random variable, but other authors do say that parameters are not that, beside this, that parameters must be calculated but the way to calculate this is very hard. My question is what of them is wrong?, if the coefficients S and K must be calculated, what is the most easy way to calculate them?.

The Cornish-Fisher expansion is a method that helps us to approximate the quantile of a target distribution $$F$$ in terms of another support distribution $$\tilde{F}$$, using the so-called cumulants of the target distribution. Cumulants are one way to (fully) describe a distribution function; i.e. if you know 'all' cumulants of a distribution function you are able recover it. Other, related, means to recover a distribution function are its (central) moments or its characteristic function.