Characterizing Tukey h and hh-Distributions through L-Moments and the L-Correlation. (12th February 2012) - Headrick, Todd C.; Pant, Mohan D.
Abstract : This paper introduces 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 nonnormal 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 correlation in terms of both relative bias and efficiency when heavy-tailed distributions are of concern.