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 the applications associated with the PM polynomials are based on the method of matching conventional 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 third-order PM distributions are developed through the method of 𝐿𝐿-moments (Hosking, 1990) using a doubling technique (Morgenthaler & Tukey, 2000) and contrasted with the method of moments in the contexts of estimation of parameters. The methodology is based on simulating uniform- and triangular-based third-order PM distributions with specified values of 𝐿𝐿 -skew and 𝐿𝐿 - kurtosis. Monte Carlo simulation results indicate that the estimators based on method of Lmoments are superior to their conventional moment-based counterparts.
Pant, Mohan D. and Headrick, Todd C. "Uniform-based and triangular-based third-order power method distributions using a doubling technique distributions." (Jan 2016).