Characterizing Tukey \(h\) and \(hh\)-distributions through \(L\)-moments and the \(L\)-correlation (Q1954437)

Summary: We introduce the Tukey family of symmetric \(h\) and asymmetric \(hh\)-distributions in the contexts of univariate \(L\)-moments and the \(L\)-correlation. Included is the development of a procedure for specifying non-normal distributions 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 (e.g., risk analysis, extreme 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 correlations in terms of both relative bias and efficiency when heavy-tailed distributions are of concern.