A Logistic L-Moment-Based Analog for the Tukey g-h, g, h, and h-h System of Distributions. (22nd October 2012) - Headrick, Todd C.; Pant, Mohan D.
Abstract : 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 γ -κ, (ii) log-logistic γ, (iii) symmetric κ, and (iv) asymmetric κ ℒ -κ ℛ . 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 γ -κ, γ, κ, and κ ℒ -κ ℛ 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 γ -κ, γ, κ, and κ ℒ -κ ℛ distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.