Volume 5, Issue 4, August 2017, Page: 147-163
On Maximum Likelihood Estimation for the Three Parameter Gamma Distribution Based on Left Censored Samples
Etienne Ouindllassida Jean Ouédraogo, Laboratory of Numerical Analysis, Informatics and Bio-mathematics (LANIBIO), Unit of Formation and Research in Exact and Applied Sciences, University of Ouagadougou, Ouagadougou, Burkina Faso
Blaise Somé, Laboratory of Numerical Analysis, Informatics and Bio-mathematics (LANIBIO), Unit of Formation and Research in Exact and Applied Sciences, University of Ouagadougou, Ouagadougou, Burkina Faso
Simplice Dossou-Gbété, Laboratory of Mathematics and Their Applications of Pau (LMAP), University of Pau and Pays de l’Adour, Pau, France
Received: May 30, 2017;       Accepted: Jun. 14, 2017;       Published: Jul. 24, 2017
DOI: 10.11648/j.sjams.20170504.14      View  1964      Downloads  182
Abstract
This paper deals with a Maximum likelihood method to fit a three-parameter gamma distribution to data from an independent and identically distributed scheme of sampling. The likelihood hinges on the joint distribution of the n − 1 largest order statistics and its maximization is done by resorting to a MM-algorithm. Monte Carlo simulations is performed in order to examine the behavior of the bias and the root mean square error of the proposed estimator. The performances of the proposed method is compared to those of two alternatives methods recently available in the literature: the location and scale parameters free maximum likelihood estimators (LSPF-MLE) of Nagatsuka & al. (2014), and Bayesian Likelihood (BL) method of Hall and Wang (2005). As in several papers on the three-parameter gamma fitting (Cohen and Whitten (1986), Tzavelas (2009), Nagatsuka & al. (2014), etc.), the classical dataset on the maximum flood levels data in millions of cubic feet per second for the Susquehanna River at Harrisburg, Pennsylvania, over 20 four-year periods from 1890–1969 from Antle and Dumonceaux’s paper (1973) is consider to illustrate the proposed method.
Keywords
Estimation, Likelihood, MM-algorithm, Order Statistics, Pearson Type III Model, Three-Parameter Gamma Model, Left Censoring
To cite this article
Etienne Ouindllassida Jean Ouédraogo, Blaise Somé, Simplice Dossou-Gbété, On Maximum Likelihood Estimation for the Three Parameter Gamma Distribution Based on Left Censored Samples, Science Journal of Applied Mathematics and Statistics. Vol. 5, No. 4, 2017, pp. 147-163. doi: 10.11648/j.sjams.20170504.14
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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