An approximate method for generating asymmetric random variables
Communications of the ACM
Adaptive Score Functions for Maximum Likelihood ICA
Journal of VLSI Signal Processing Systems
Computational Statistics & Data Analysis
Estimating the parameters of a generalized lambda distribution
Computational Statistics & Data Analysis
Numerical maximum log likelihood estimation for generalized lambda distributions
Computational Statistics & Data Analysis
L-moments and TL-moments of the generalized lambda distribution
Computational Statistics & Data Analysis
Cressie and Read power-divergences as influence measures for logistic regression models
Computational Statistics & Data Analysis
Estimation of quantile mixtures via L-moments and trimmed L-moments
Computational Statistics & Data Analysis
Confidence intervals for quantiles using generalized lambda distributions
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
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The generalized lambda distribution (GLD) is a flexible four parameter distribution with many practical applications. L-moments of the GLD can be expressed in closed form and are good alternatives for the central moments. The L-moments of the GLD up to an arbitrary order are presented, and a study of L-skewness and L-kurtosis that can be achieved by the GLD is provided. The boundaries of L-skewness and L-kurtosis are derived analytically for the symmetric GLD and calculated numerically for the GLD in general. Additionally, the contours of L-skewness and L-kurtosis are presented as functions of the GLD parameters. It is found that with an exception of the smallest values of L-kurtosis, the GLD covers all possible pairs of L-skewness and L-kurtosis and often there are two or more distributions that share the same L-skewness and the same L-kurtosis. Examples that demonstrate situations where there are four GLD members with the same L-skewness and the same L-kurtosis are presented. The estimation of the GLD parameters is studied in a simulation example where method of L-moments compares favorably to more complicated estimation methods. The results increase the knowledge on the distributions that belong to the GLD family and can be utilized in model selection and estimation.