I-Divergence Based Statistical Inference For Heteroscedasticity And Compounds Of Arsenic Contamination In Chile

Arsenic and arsenic compounds contamination is at present a topic of great importance in the field of water quality. Simply applying ANOVAs to test the hypothesis of mean heterogeneity of arsenic contamination in water may lead to oversimplifications, since data can be skewed and the power of many tests will be affected by this skewness. In order to overcome such a problem, we introduce a novel heterogeneity measure of arsenic contamination. This measure is based on the correlation between two univariate statistics decomposed from the Kullback-Leibler divergence of sampled vector as compared to the canonical parameter. For the Gamma distribution, the mere detection of heterogeneity in the means or variances is akin to an omnibus test for mean differences in a standard ANOVA, so our method is useful in this regard. We illustrate this measure's applicability and usefulness in assessment of pollutant compounds. Subsampling and resampling algorithms are developed in order to facilitate a study in a one sample setting. The method is applied to a heteroscedasticity assessment of the arsenic contamination of potable water from the rural area of the region of Arica and Parinacota, Chile.