Alternative Tools of Statistical Analysis: L-moments and TL-moments of Probability Distributions

Abstract

This paper deals with an alternative method to characterize some probability distribution, i.e. L-moments and TL-moments. Moments and cumulants were commonly used for this purpose before. Moment method of parameter estimation is indeed very simple, but it is very inaccurate, especially if there are the moments of the third or higher order. These problems mainly occur in the case of small samples. Maximum likelihood method has been considered as the most accurate method of parameter estimation for a long time. Using the method of L-momednts gives more accurate results than using the maximum likelihood method in many cases when estimating parameters of probability distribution. The method of TL-moments brings still more accurate results than the method of L-moments. This paper deals with these three methods of parameter estimation and with the comparison of their accuracy. Three-parametric lognormal curves constitute basic probability distribution. They were used as the model distribution of income in the Czech Repubublic in 1992, 1996, 2002 and 2004−2007.