Power method (PM) polynomials have been used for simulating non-normal distributions in a variety of settings such as toxicology research, price risk, business-cycle features, microarray analysis, computer adaptive testing, and structural equation modeling. A majority of these applications are based on the method of matching product moments (e.g., skew and kurtosis). However, estimators of skew and kurtosis can be (a) substantially biased, (b) highly dispersed, or (c) influenced by outliers. To address this limitation, two families of double-uniform-PM and double-triangular-PM distributions are characterized through the method of 𝐿-moments using a doubling technique. The 𝐿-moment based procedure is contrasted with the method of product moments in the contexts of fitting real data and estimation of parameters. A methodology for simulating correlated double-uniform-PM and double-triangular-PM distributions with specified values of 𝐿-skew, 𝐿-kurtosis, and 𝐿-correlation is also demonstrated. Monte Carlo simulation results indicate that the L-moment-based estimators of 𝐿-skew, 𝐿-kurtosis, and 𝐿-correlation are superior to their product moment-based counterparts.
Mathematics Subject Classification: 60E05; 62G30; 62H12; 62H20; 65C05; 65C10; 65C60; 78M05
Keywords: Product moments; Pearson correlation; 𝐿-moments; 𝐿-correlation