Cornish–Fisher expansion

The Cornish–Fisher expansion is a mathematical technique used in statistics to approximate the quantiles of a probability distribution through its moments (mean, variance, skewness, and kurtosis) or its cumulants. It is particularly useful for adjusting standard normal quantiles to account for non-normality in distributions. In essence, the expansion transforms the quantiles of the standard normal distribution (which assumes a Gaussian shape) to those of a non-normal distribution by incorporating information about the distribution's shape.