L-moments of asymmetric generalized distributions obtained through quantile splicing

Abstract

Balakrishnan et al. (Communications in Statistics Simulation and Computation 46 (2017) 4082–4097) proposed a skew logistic distribution by making use of the cumulative distribution function (CDF) of the folded logistic distribution. They made use of moments of order statistics from the standard folded logistic distribution to obtain the single and product moments of order statistics from the skew logistic distribution. Subsequently, Mac’Oduol et al. (Communications in Statistics—Theory and Methods 49 (2020) 4413–4429) proposed quantile splicing for the construction of two-piece distributions using quantile functions of symmetric distributions as building blocks. This paper presents the derivation of a general formula for the L-moments of such two-piece distributions. In addition, quantile splicing and its results are then specialized to the Tukey lambda distribution, and an example is used to illustrate the results developed.