Small-sample estimators of the quantiles of the normal, log-normal and Pareto distributions

Estimators of the quantiles of the normal and log-normal distributions are derived. They are more efficient than the established estimators by a wide margin for small samples and high quantiles of the log-normal distribution. Although their evaluation is iterative, it requires only moderate amount of computing, which is not related to the sample size. The method is also applied to the quantiles of the Pareto distribution, but the resulting estimator is more efficient only in some settings. An application to financial statistics, estimating the return on a unit investment in equity markets over a long term, is presented.