Estimation of distributional parameters for censored trace level water quality data. 1. Estimation Techniques
A recurring difficulty encountered in investigations of many metals and organic contaminants in ambient waters is that a substantial portion of water sample concentrations are below limits of detection established by analytical laboratories. Several methods were evaluated for estimating distributional parameters for such censored data sets using only uncensored observations. Their reliabilities were evaluated by a Monte Carlo experiment in which small samples were generated from a wide range of parent distributions and censored at varying levels. Eight methods were used to estimate the mean, standard deviation, median, and interquartile range. Criteria were developed, based on the distribution of uncensored observations, for determining the best performing parameter estimation method for any particular data det. The most robust method for minimizing error in censored-sample estimates of the four distributional parameters over all simulation conditions was the log-probability regression method. With this method, censored observations are assumed to follow the zero-to-censoring level portion of a lognormal distribution obtained by a least squares regression between logarithms of uncensored concentration observations and their z scores. When method performance was separately evaluated for each distributional parameter over all simulation conditions, the log-probability regression method still had the smallest errors for the mean and standard deviation, but the lognormal maximum likelihood method had the smallest errors for the median and interquartile range. When data sets were classified prior to parameter estimation into groups reflecting their probable parent distributions, the ranking of estimation methods was similar, but the accuracy of error estimates was markedly improved over those without classification.
- Research Organization:
- Geological Survey, Reston, VA
- OSTI ID:
- 5394352
- Journal Information:
- Water Resour. Res.; (United States), Vol. 22:2
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
STATISTICAL MODELS
PERFORMANCE TESTING
WATER QUALITY
DATA ANALYSIS
COMPARATIVE EVALUATIONS
CONTAMINATION
METALS
MONTE CARLO METHOD
ORGANIC COMPOUNDS
POLLUTANTS
REGRESSION ANALYSIS
ELEMENTS
ENVIRONMENTAL QUALITY
MATHEMATICAL MODELS
MATHEMATICS
STATISTICS
TESTING
520100* - Environment
Aquatic- Basic Studies- (-1989)