Results of Simulation Experiments with Data Sets with Low Means. One hundred values were randomly drawn from data populations with low means, and a control level (i.e., the 99th percentile) was calculated using the different approaches. Then how much of the remaining data population could be covered by these calculated control levels was assessed and compared to the percentile of interest (e.g., if a calculation approach covered 98% of the data population for a 99th percentile of interest, then the error would be 1%). Furthermore, a Chi-squared goodness-of-fit test was performed in order to identify the best-fitting parametric model for each data set, and the coverage of the control levels calculated always using the best-fitting model was assessed (indicated as “Best fit” in the table).
| Data Set | Normal Distribution | Poisson Distribution | Negative Binomial Distribution | ZINB | Gamma Distribution | Formula by Hussong and Madsen | Non-Parametric Percentile | Best fit (Chi-squared test) |
|---|---|---|---|---|---|---|---|---|
| x̄ = 0.34; N = 247 | 1.78% | 2.91% | 0.74% | 0.95% | 0.68% | 1.03% | 1.22% | 0.7% |
| x̄ = 0.27; N = 465 | 0.67% | 1.11% | 0.23% | 0.28% | 0.45% | 0.34% | 0.64% | 0.2% |
| x̄ = 0.91; N = 559 | 1.09% | 3.47% | 0.67% | 0.67% | 0.61% | 1.51% | 0.54% | 0.65% |
| x̄ = 0.14; N = 1949 | 0.75% | 0.87% | 0.43% | 0.43% | 0.36% | 0.22% | 0.57% | 0.43% |
| x̄ = 0.47; N = 210 | 1.23% | 2.04% | 0.95% | 0.95% | 0.62% | 1.23% | 0.98% | 0.9% |
| x̄ = 0.02; N = 322 | 1.30% | 1.19% | 1.19% | 1.19% | 1.12% | 1.12% | 1.12% | 1.19% |
| x̄ = 0.10; N = 730 | 1.11% | 1.21% | 0.80% | 0.80% | 0.44% | 0.72% | 0.69% | 0.80% |
| x̄ = 0.11; N = 738 | 1.03% | 1.04% | 0.69% | 0.57% | 0.24% | 0.47% | 0.37% | 0.69% |
| Average of all data sets | 1.12% | 1.73% | 0.71% | 0.73% | 0.56% | 0.83% | 0.77% | 0.71% |