Advances and Applications in Statistics
Volume 7, issue 2, Pages 193 - 209
(August 2007)
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ORTHOGONAL PROJECTION L-MOMENT ESTIMATORS FOR THREE-PARAMETER DISTRIBUTIONS
S. El Adlouni (Canada), T. B. M. J. Ouarda (Canada) and B. Bobé¥ (Canada)
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Abstract: A new L-moment estimation method for the parameters of three-parameter distributions is presented. Traditional L-moment estimators of a statistical distribution?s parameters are based on the solution of the system of equations obtained by equating sample and distribution L-moments. For three-parameter distributions, the third equation equates the sample and distribution
Graphically, on the L-moment diagram, this is equivalent to considering the vertical projection of the point that represents the sample on the fitted distribution curve. Approximate solutions to the system are then obtained by Hosking and Wallis [8]. The present work proposes a new approach, termed the Orthogonal Projection L-moment estimator that is applicable for three-parameter distributions. The new estimator is based on the identification of the closest point on the fitted distribution curve to the sample point, in terms of Euclidean distance. This is equivalent to considering the orthogonal projection of the point that represents the sample on the fitted distribution curve. This paper presentsalso theresults of a simulation experiment aimed atcomparing the two L-moment estimators in the case of known and unknown parent distributions. It is shown that this new estimator leads to an improvementintheestimationofdistributionparametersandquantiles. |
Keywords and phrases: L-moments, projection, Euclidean distance, three-parameter distribution, estimation, parameter, projection, simulation. |
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