An investigation of L-moments and the generalized logistic distribution: applied as a new way to model ice strength

Bartholomew, Linda (1995) An investigation of L-moments and the generalized logistic distribution: applied as a new way to model ice strength. Masters thesis, Memorial University of Newfoundland.

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Abstract

In cold ocean research the development of statistical techniques useful in the analysis of cold ocean data such as ice strength is of important practical concern. A central interest is the identification of and fitting of suitable models to the data, for the analysis of such data. In this practicum we study the theory of L-Moments as a method of distributional identification and parameter estimation. In particular, the Generalized Logistic Distribution (GLD) is fitted to nine data sets consisting of breaking strength measurements of different types of ice using the method of L-Moments. The results compare favorably to the original analysis of the data based on Maximum Likelihood fitting of the Weibull distribution. The asymptotic distribution of the L-Moment estimators is derived, and a test for the symmetry of the GLD, based on these asymptotic results, is developed. A Monte Carlo simulation study demonstrates the performance of the method of L-Moments for the estimation of the parameters of the GLD and compares it to the method Maximum Likelihood and the method of Moments. L-Moment estimators are easy to compute and perform consistently well across a wide range of parameter values. The method was found to be a simple and reliable method for estimation and distributional identification and thus it provides an attractive alternative method to the standard techniques. The application of this method to real data illustrates the implementation of the method and the contexts in which the method is useful.

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