Table 1 Maximum discrepancy in the approximating normal CDF, for sample size 100, in terms of Berry-Esséen bounds, and via computation
Distribution | Parameter estimates | Maximum error | ||
|---|---|---|---|---|
Berry-Esséen | Exact CDF | |||
Negative Binomial | k | μ | ||
0.05 | 0.05 | 28.9% | 12.5% | |
0.1 | 27.9% | 9.8% | ||
10 | 27.3% | 6.1% | ||
50 | 27.3% | 6.0% | ||
0.1 | 0.05 | 22.3% | 11.9% | |
0.1 | 20.6% | 8.8% | ||
10 | 19.5% | 4.4% | ||
50 | 19.5% | 4.4% | ||
0.5 | 0.05 | 15.7% | 11.3% | |
0.1 | 12.5% | 8.3% | ||
10 | 9.4% | 2.1% | ||
50 | 9.4% | 1.9% | ||
Poisson | μ | |||
0.05 | 13.7% | 11.6% | ||
0.1 | 9.8% | 8.2% | ||
10 | 4.9% | 3.2% | ||
50 | 4.9% | 1.5% | ||
Binomial | μ | |||
( d = 1) | 0.05 | 19.5% | 11.6% | |
0.1 | 12.8% | 8.3% | ||
0.5 | 4.7% | 4.0% | ||