Abstract
Various mathematical models have been developed to reveal the influence of pollution sources on natural environment. Among them, this paper states Chemical Mass Balance (CMB), which is a model to estimate source contribution rates based on the mass balance between certain materials at sources and those at a receptor site. As its solution, linear least-squares technique, that is, multiple regression has been widely used. The compositions of materials observed at sources and at a receptor site are assumed for independent and dependent variables, respectively. However, the observations at sources involve irregular variation as same as in that at a receptor site. Multiple regression cannot deal with such irregular variation. Other than this problem, existing methods involve several problems. To solve those problems, this paper proposes two kinds of functional relationship models for CMB. One is a model based on the mass, and another is a model based on the proportion. The use of multinomial and scaled Dirichlet distributions is also proposed to define the covariance structure in the later model. Finally, the proposed models are applied to actual dioxins data.
