On the sensitivity of entropy weight to sample statistics in assessing water quality: statistical analysis based on large stochastic samples

Entropy weight (EW) has been widely adopted in water quality assessment. To quantitatively determine the effects of sample statistics on entropy weight, a statistical analysis based on 1002 stochastic samples was carried out to reveal the relationships of EW with sample mean, standard deviation (SD) and coefficient of variation (CV) in this study. Two modes (varied sample number mode and fixed sample number mode) under which the study was carried out were assumed. Sensitivity of EW to sample range was also investigated by perturbation approach. The study has shown that the correlations of EW with mean, SD and CV under varied sample number mode are insignificant, while under fixed sample number mode a significant quadratic relationship between EW and mean, and a significant linear relationship between EW and SD can be found. The relationship of EW with CV shows a check-mark-shaped pattern, and can be expressed by mixed quadratic and linear equations. The variation of sensitivity of EW to sample range can be expressed by quadratic equations. This study falls within the scope of sensitivity analysis, and is of great value in promoting the development of uncertainty theory and the research of sensitivity analysis associated with water quality assessment and other environmental studies such as environmental hazard evaluation, environmental risk assessment, environmental data interpretation and environmental policy making.