Likelihood and objective Bayesian modeling of acidity and major ions in rainfall using a bivariate pseudo-Gamma distribution

Modeling the acidity in rainfall at certain locations is a complex task because of different environmental conditions for different rainfall regimes and the large variability in the covariates involved. In this paper, concentration of acidity and major ions in the rainfall in UK is analyzed by assuming a bivariate pseudo-Gamma distribution. The model parameters are estimated by using the maximum likelihood method and the goodness of fit is checked. Furthermore, the non-informative Jeffreys prior for the distribution parameters is derived and a hybrid Gibbs sampling strategy is proposed to sample the corresponding posterior for conducting an objective Bayesian analysis. Finally, related quantities such as the deposition flux density are derived where the general pattern of the observed data appears to follow the fitted densities closely.