Proyecciones Journal of Mathematics Vol. 30, N^o 3, pp. 415-439, December 2011. Universidad Catolica del Norte Antofagasta - Chile

 

A proposed reparametrization of gamma distribution for the analysis of data of rainfall-runoff driven pollution

 

B. Lagos Álvarez, G. Ferreira, M. Valenzuela Hube

Universidad de Concepcion, Chile

 

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ABSTRACT

A generalized gamma (GG) distribution of four parameters was first introduced by Amoroso 1925, and since then, different distributions emerged as subclasses of this model. This model is commonly usedtomodellifetimedataordatawitharightskewedunimodalden-sity function. In this article, we use a reparameterization of the GG distribution that is compared with other usual two-parameter distributions, Weibull, generalized exponential (Gupta and Kundu 1999), and gamma, using a real data set with a high coefficient of asymmetry and kurtosis (Valenzuela M. 2009). Akaike's information criterion and Bayesian information criterion indicates that our reparametrization of the gamma distribution is better. Besides a Monte Carlo simulation study, shows the behavior of five estimation methods: least squared, weighted least squared, moments, probability weighted moments and maximum likelihood methods.

Keywords : Gamma distribution, Maximum likelihood estimators, Moment estimators, Probability weighted moment estimators, Weighted least squares estimators, Water pollution and watershed.

 

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B. Lagos-Álvarez

Department of Statistic, University of Concepcion Esteban Iturra, Barrio Universitario,

Chile

e-mail : bla@udec.cl

G. Ferreira

Department of Statistic, University of Concepcion Esteban Iturra, Barrio Universitario,

Chile

e-mail : gpferrei@puc.cl

M. Valenzuela-Hube

Environmental Sciences Center EULA, University of Concepcion,

Chile

e-mail : marvalenz@udec.cl

Received : March 2011. Accepted : October 2011