Improved estimators for analyzing highly skewed environmental datasets with detection limits

Abstract

The datasets from environmental studies often contain some measurements that fall below some detection limits. These datasets are often highly skewed making most of the standard models inappropriate to model these data. In order to investigate such data, the mixture models under classical methods have been proposed in the literature. In the case of mixture models, the mixture of gamma and lognormal models has frequently been used. We have proposed the mixture model under the Bayesian approach to analyze the said datasets. Two real skewed datasets with detection limits have been used for the analysis. On comparing with a variety of mixture models, the two-component mixture of Frechet distributions (2CMFD) has been explored to be the most suitable model for modelling highly skewed datasets. In addition, the performance of the proposed Bayes estimators was better than that of those existing in the literature.