Mathematical modeling of environmental data

Environmental pollution studies conducted to monitor ambient levels and to quantify the concentration of various pollutants entering a given environmental area are of great interest for possible adverse-health effects. Of particular importance in environmental data analysis is to select appropriate probability models. The previous studies indicate that none of the probability models, including the classical log-normal, has been identified to be superior to others in a general sense. To address this problem, the purpose of this paper is twofold. First, we introduce a generalized log-logistics distribution as a general model in fitting environmental pollutant data. The family of the generalized log-logistics distribution includes several well-known distributions in modelling data of environmental pollutant concentrations, such as log-normal, Weibull, and gamma as special cases. Second, by applying the proposed model to some environmental data sets, we explore the possibilities of using this model as a general probability model for fitting environmental-quality data.