Contamination severity index: An analysis of Bangladesh groundwater arsenic

This article deals with the measurement of groundwater arsenic ($As$) contamination. The focus is on using a proper index for the severity of contamination, rather than just using the proportion of observations above a threshold level. We specifically focus on the contamination severity index (CSI) proposed by Sen (2016. Sankhya B, 78B(2), 341–361.). An alternative estimator in contrast to the one given by Sen (2016. Sankhya B, 78B(2), 341–361.) is used here which is useful for a small number of observations. The data used is that collected by the British Geological Society and the Bangladesh Department of Public Health Engineering during 1997–2001. Their analysis was based on the simple proportion of the observations above a threshold level, whereas the CSI measure adequately takes into account the severity of the observations. It is emphasized in this article that the comparison of areas with average arsenic ($As$) levels to determine arsenic severity is not appropriate in general due to a large variation in the sample values due to the depth of wells. However, an alternative to the CSI proposed in Sen (2016. Sankhya B, 78B(2), 341–361.) has been given in this article that takes into account the depth of wells corresponding to the $As$ samples. This article also uses the bootstrap methodology in assessing the bias and standard errors of the estimators, and the corresponding bias-corrected and accelerated confidence intervals.