Date of Award


Document Type


Degree Name

Master of Science in Operations Research


Department of Operational Sciences

First Advisor

Edward F. Mykytka, PhD


The Generalized Lambda Distribution GLD is a four-parameter, continuous probability distribution that is useful for simulation analysis. The strengths of the GLD lie in its abilities to approximate many distributions, represent data when the underlying distribution is unknown, and fit or generate random variates. The method of moments is presently the accepted technique for estimating the parameters of this distribution. However, it is sensitive to extreme observations and subject to large sampling variability as the sample size decreases. L-moments are expectations of certain linear combinations of order statistics. They can be used to estimate parameters and quantiles of probability distributions. Their main advantage over conventional moments is that they suffer less from the effects of sampling variability, and are theoretically more robust to outliers than conventional moments. Estimating the parameters of the GLD by matching its L-moments to those of the sample is known as the method of L-moments. This appears to be an attractive alternative to the method of moments and is developed in this thesis. A Monte Carlo experiment compared the method of L-moments to the method of conventional moments and a third method which uses alternate measures of symmetry and tailweight. Experiment results showed that L-moments are better than conventional and alternate moments for fitting distributions to sample data, particularly when the skewness and kurtosis of the sample distribution are large.

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