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

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Abstract

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.

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Acknowledgments

This research was supported by the Doctoral Postgraduate Technical Project of Chang’an University (2014G5290001 and 2013G5290002) and the National Natural Science Foundation of China (41172212). We are grateful to Dr. Renato Mendoza S for his valuable comments and detailed editing of the original manuscript, which have helped us a lot in improving the quality of our research. The anonymous reviewers are also acknowledged for their valuable comments.

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Authors and Affiliations

  1. School of Environmental Science and Engineering, Chang’an University, No. 126 Yanta Road, Xi’an, 710054, Shaanxi, China

    Jianhua Wu, Peiyue Li, Hui Qian & Jie Chen

  2. Key Laboratory of Subsurface Hydrology and Ecological Effect in Arid Region of the Ministry of Education, Chang’an University, No. 126 Yanta Road, Xi’an, 710054, Shaanxi, China

    Jianhua Wu, Peiyue Li, Hui Qian & Jie Chen

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  1. Jianhua Wu
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Correspondence to Peiyue Li.

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Wu, J., Li, P., Qian, H. et al. On the sensitivity of entropy weight to sample statistics in assessing water quality: statistical analysis based on large stochastic samples. Environ Earth Sci 74, 2185–2195 (2015). https://doi.org/10.1007/s12665-015-4208-y

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  • DOI: https://doi.org/10.1007/s12665-015-4208-y

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