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

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 used to model life time data or data with a right skewed unimodal density 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.