A-38 
Pru|»rtiaii of 
Figure 5.1. A family of curves illustrating the behavior of the CFD as the population mean 
decreases from the criterion threshold. The parameter values for each curve and the 
corresponding curve number are given in Table 5.1. 
Note that when the population mean is equal to the criterion threshold, the CFD is a 
diagonal line from upper left to lower right (Figure 5.1, curve 1). This is largely an 
artifact of using symmetric distributions, the normal, for both the time and space 
variance components. That is, when the population median is equal to the criterion 
threshold, we expect an average of 50% noncompliance over time and we expect the 
exceed 50% noncompliance 50% of the time. 
As the overall population mean decreases from the criterion threshold, the family of 
curves tends to move from the diagonal line toward the lower left comer. Thus a 
reference population, which should have a small probability of exceeding the crite¬ 
rion threshold might have a shape similar to the green curve. This illustrates the 
importance of the shape of the CFD in measuring compliance. A CFD from a highly 
compliant population will tend to hug to lower left comer similar to the blue and 
green curves. As the population mean approaches the criterion threshold, the CFD 
approaches curve 1. If the population mean were to exceed the criterion threshold, 
the CFD would tend toward the upper right corner. 
appendix a 
The Cumulative Frequency Diagram Method for Determining Water Quality Attainment 
