Abstract
Consider the estimation of a tail percentile or tail quantile from the moments of a continuous random variable. If a normal approximation to the distribution of the variable is applicable then an adequate result is found easily using the mean and variance. However, the use of higher moments would be expected to give a better result. We describe and evaluate two different procedures for estimating tail quantiles, the first of which uses the Pearson system of distributions and moments up to order 4, and the second of which uses the Cornish-Fisher expansion and moments up to order 8. Neither method is uniformly superior.