The Properties of L-moments Compared to Conventional Moments

Abstract

In this thesis, we survey the concept of L-moments. We introduce the deflnition of L-moments and the probability weighted moments (PWMs) and then we expressed the L-moments by the use of the probability weighted moments. Also, we established the relation between the L-moments and the order statistic. Moreover, we introduced some of the properties the L-moments especially the property that, if the mean of the distribution exists, then all of the L-moments exist and uniquely deflne the distribution. That is, no two distinct distributions have the same L-moments. This property is not always valid in the conventional moments. Moreover, we flnd the L-moments for some distributions. Later, we introduce estimation for the L-moments and probability weighted moments and then we used them in estimating the parameters of some distributions as the Uniform distribution, the Exponential distribution, Generalized Logistic distribution and Generalized Pareto Distribution. Moreover, we introduce the generalized lambda distribution (GLD) and we flnd the (PWMs) and L-moments for (GLD). Also, we deflned the Censored Data which is divided into two cases: I-Right censoring and II-Left censoring and then we flnd the partial property weighted moments (PPWMs) for both cases. Finally, we flnd the type B PPWMs for GLD.