Alternative Way of Statistical Data Analysis: L-Moments and Tl-Moments of Probability Distribution

Abstract

Moments and cumulants are commonly used to characterize the probability distribution or observed data set. Th e use of the moment method of parameter estimation is also common in the construction of an appropriate parametric distribution for a certain data set. Th e moment method does not always produce satisfactory results. It is diffi cult to determine exactly what information concerning the shape of the distribution is expressed by its moments of the third and higher order. In the case of small samples in particular, numerical values of sample moments can be very diff erent from the corresponding values of theoretical moments of the relevant probability distribution from which the random sample comes. Parameter estimations of the probability distribution made by the moment method are oft en considerably less accurate than those obtained using other methods, particularly in the case of small samples. Th e present paper deals with an alternative approach to the construction of an appropriate parametric distribution for the considered data set using order statistics.