A method for simulating nonnormal distributions with specified \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation
Summary: We introduce two families of distributions referred to as the symmetric \(\kappa\) and asymmetric \(\kappa_{\mathcal L}-\kappa_{\mathcal R}\) distributions. The families are based on transformations of standard logistic pseudo-random deviates. The primary focus of the theoretical development is in the contexts of \(L\)-moments and the \(L\)-correlation. Also included is the development of a method for specifying distributions with controlled degrees of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation. The method can be applied in a variety of settings such as Monte Carlo studies, simulation, or modeling events. It is also demonstrated that estimates of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation are superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when moderate-to-heavy-tailed distributions are of concern.
standard logistic pseudo-random deviates
scientific article; zbMATH DE number 6172996
scientific article