This paper introduces the Tukey family of symmetric and asymmetric -distributions in the contexts of univariate -moments and the -correlation. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -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 -skew, -kurtosis, and -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.
