Confidence of compliance: parametric versus nonparametric approaches

• Published in: Water research (Oxford) Vol. 37; no. 15; pp. 3666 - 3671
• Main Author: McBride, Graham B.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.09.2003; Elsevier Science
• Subjects: Applications; Applied sciences; Bayes Theorem; Bayesian probability; Classical probability; Consumer's risk; Exact sciences and technology; Global environmental pollution; Guideline Adherence; Humans; Mathematics; Nonparametric; Parametric; Percentile standards; Pollution; Probability and statistics; Reliability, life testing, quality control; Reproducibility of Results; Risk Assessment; Sciences and techniques of general use; Statistics; Supplier's risk; Water Pollutants - analysis; Water Pollutants - toxicity; Water Supply; Supplier's risk; Nonparametric; Percentile standards; Consumer's risk; Bayesian probability; Classical probability; Parametric; Bayes estimation; Parametric method; Drinking water; Pollution; Statistical analysis; Consumer; Water quality; Non parametric method; Environment; Supplier; Risk analysis; Sampling
• ISSN: 0043-1354; 1879-2448
• DOI: 10.1016/S0043-1354(03)00272-0

Previous classical and Bayesian formulations of compliance assessment rules based on a nonparametric approach are compared with formulations based on the assumption that compliance assessment data have been randomly drawn from a normal population with unknown mean and variance. Graphs of parametric (Bayesian) “Confidence of Compliance” curves are presented. With one exception it is concluded that compliance rules based on a nonparametric approach are the more robust, as their formulation does not depend on any assumption as to the nature of the parent distribution and because rules devised under either approach are generally similar. The exception occurs for rules based on minimizing the consumer's risk (i.e., environment's risk) when a large number of samples are to hand and goodness-of-fit tests give strong grounds for the assumption of a normal parent. In that case the parametric compliance rule—either Bayesian or classical—becomes rather less strict.