Journal article
Influence of outlying observations on selected estimates of parameters of distributions
Ground Water, Vol.26(3), pp.325-332
1988
DOI: 10.1111/j.1745-6584.1988.tb00396.x
Abstract
Most measures of ground-water quality are positively skewed with a few observations occurring with significantly large values. Using a set of mathematical expressions and readily available software, the effect of deleting one or more large-valued observation(s) on selected estimates of parameters of underlying distributions are evaluated. The effect of deleting a single large-valued observation on the mean is linear, and on the standard deviation it is nonlinear (approximately quadratic). In the case of multiple deletions, the effect of sum of the large-valued observations on the mean is linear and on the standard deviation it is nonlinear. The effect on the standard deviation is a function of the sum of squares of deleted observations. The standard deviation is much more sensitive to the magnitude of deleted observations than the mean. Analysis of a large data set consisting of 17 primary and secondary drinking-water constituents showed that (with a few exceptions) the effect of deleting large-valued observations on the standard deviation is considerably higher than that on the mean, the 95th and the 99th percentiles. Seldom are percentiles below the 75th affected by the deletion of large-valued observations. Analyses of upper quantiles and the maximum can be of much value in the study of maximum contaminant level (MCL) violations and population exposures to toxic chemicals above and beyond certain threshold levels. Since large-valued observations affect the estimates of different parameters differently, it is extremely important to choose the relevant parameter first and then study the change in its estimate based on the deletion of large-valued observations.
Note: For the sake of brevity, the terms mean, standard deviation, and quantiles (or percentiles) are often used in this paper, instead of the more precise estimated mean, estimated standard deviation, and estimated quantiles (or percentiles).
Details
- Title: Subtitle
- Influence of outlying observations on selected estimates of parameters of distributions
- Creators
- R. Rajagopal - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Ground Water, Vol.26(3), pp.325-332
- DOI
- 10.1111/j.1745-6584.1988.tb00396.x
- ISSN
- 0017-467X
- Language
- English
- Date published
- 1988
- Academic Unit
- Civil and Environmental Engineering; Geographical and Sustainability Sciences
- Record Identifier
- 9983557266402771
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