On Maximum Likelihood Estimation for the Three Parameter Gamma Distribution Based on Left Censored Samples

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.