Comparison of Estimates Using L and TL Moments and Other Robust Characteristics of Distributional Shape and Tail Heaviness

Abstract

Correct identification of a probability distribution is crucial in many areas of parametric statistics, inappropriate choice of the model can result in misleading or even incorrect decisions. In the text, we study the performance of robust characteristics of skewness and kurtosis of probability distributions that are less sensitive to outliers than the characteristics based on classical product moments. We use Monte Carlo simulation to illustrate properties of various robust (mainly quantile type) characteristics of skewness and kurtosis and compare them to the L-skewness (TL-skewness) and L-kurtosis (TL-kurtosis). The bias, standard and mean squared error of estimators are compared using simulations for standard normal, Laplace, Student, gamma and beta distributions and sample sizes ranged from 10 to 500 observations. The selected distributions gain symmetric and asymmetric unimodal distributions with different tail heaviness.