الفهرس 
Chapter 1 IntroductionOnly 14 pages are availabe for public view
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Abstract
The generalized lambda distribution (GLD) is a simple and flexible distribution that can assume a wide range of shapes. Four different estimation methods of the GLD were considered, the method of moments, the method of percentiles, the method of L-moments and the method of trimmed L-moments. General formulae for L-moments and TL-moments up to the rth order have been derived. The trimming proportion in case of TL-moments has been generalized to accommodate both symmetric and asymmetric trimming. Eleven Matlab algorithms were written to search for GLD parameters that minimize the difference between sample estimates and GLD counterparts for a best-fit to the sample at hand. A simulation study was run comparing the four estimation methods. Simulated random samples were generated from the standard normal, the exponential, the Gamma distributions and five selected cases of the GLD. Goodness of fit tests were conducted ”one and two samples Kolmogorov-Smirnov tests” to judge the quality of fit obtained. An application to model the river Nile flood data was performed. Both L-moments and TL-moments estimation methods proved to be more robust to the presence of outliers and over-performed other methods especially in the case of small samples but at the expense of higher variability ”higher mean squared error”.