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

Abstract EN

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 κℒ-κℛ.

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 κℒ-κℛ 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 κℒ-κℛ distributions are substantially superior to their corresponding conventional product-moment estimators in terms of relative bias and relative standard error.