A Logistic -Moment-Based Analog for the Tukey -, , , and - System of Distributions

This paper introduces a standard logistic L -moment-based system of distributions. The proposed system is an analog to the standard normal conventional moment-based Tukey g-h , g , h , and h-h system of distributions. The system also consists of four classes of distributions and is referred to as (i) asymmetric -, (ii) log-logistic , (iii) symmetric , and (iv) asymmetric -. The system can be used in a variety of settings such as simulation or modeling events—most notably when heavy-tailed distributions are of interest. A procedure is also described for simulating -, , , and - distributions with specified L -moments and L -correlations. The Monte Carlo results presented in this study indicate that estimates of L -skew, L -kurtosis, and L -correlation associated with the -, , , and - distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.