Fitting Distributions and Data with the GLD through L -Moments

Authored by: Zaven A. Karian , Edward J. Dudewicz , Kunio Shimizu

Handbook of Fitting Statistical Distributions with R

Print publication date:  October  2010
Online publication date:  April  2016

Print ISBN: 9781584887119
eBook ISBN: 9781584887126
Adobe ISBN:

10.1201/b10159-9

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Abstract

L-moments, defined as linear combinations of expectations of order statistics, are useful in fitting distributions because they specify location, scale, and shape (symmetry and kurtosis) attributes like ordinary moments do. An advantage of L-moments is that they exist whenever the underlying random variable has a finite mean, enabling the use of L-moments when ordinary moments are not available. A difficulty in fitting a GLD through the method of moments is the complexity of the equations that need to be solved to determine the GLD parameters. Here too, the use of L-moments provides an advantage since the equations associated with the determination of the GLD parameters, although not trivial, are simpler than the ones associated with fitting a GLD through moments.

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