A doubling method for the generalized lambda distribution (Q1954415)

Summary: We introduce a new family of generalized lambda distributions (GLDs) based on a method of doubling symmetric GLDs. The focus of the development is in the context of \(L\)-moments and \(L\)-correlation theory. As such, included is the development of a procedure for specifying double GLDs with controlled degrees of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlations. The procedure can be applied in a variety of settings such as modeling events and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy tailed distributions are of concern.