ABSTRACT:Cumulative density functions (c.d.f.'s) for water quality random variables may be estimated using data from a routine grab sampling program. The c.d.f. may then be used to estimate the probability that a single grab sample will violate a given stream standard and to determine the anticipated number of violations in a given number of samples. Confidence limits about a particular point on the c.d.f. may be used to reflect the accuracy with which the sample estimate represents the true c.d.f. Methods are presented here for calculating such confidence limits using both a normal model and a nonparametric model. Examples are presented to illustrate the usefulness of an estimated c.d.f. and associated confidence limits in assessing whether an observed number of standard violations is the result of natural variability or represents real degradation in water quality.
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