Table 3.
Dependence of fitting methods on sample size using simulated data with a double exponential PDF.
| Data points | Number of Bins | Bin Size | Parameter | Maximum Likelihood Results* |
Nonlinear Least Squares Results* |
R2/Adj R2 |
|---|---|---|---|---|---|---|
| 100000** | 1000 | Equal (1 s/bin) | a1 = 0.75 | 0.74 (0.74–0.74) | 0.72 (0.72–0.72) | 0.0.9997/0.9997 |
| τ1 = 10 s | 10.9 (10.9–10.9) | 10.2 (10.1–10.2) | ||||
| τ2 = 100 s | 101.8 (100.3–103.1) | 123.4 (120.6–126.1) | ||||
| 10000** | 1000 | Equal (1 s/bin) | a1 = 0.75 | 0.75 (0.73–0.76) | 0.73 (0.69–0.72) | 0.0.9975/0.9975 |
| τ1 = 10 s | 10.9 (10.5–11.3) | 10.2 (10.1–10.2) | ||||
| τ2 = 100 s | 102.7 (107.5–97.1) | 122.0 (114.7–130.1) | ||||
| 10000* | 15 | Variable | a1 = 0.75 | 0.75 (0.73–0.76) | 0.76 (0.74–0.79) | 0.0.9999/0.9999 |
| τ1 = 10 s | 10.9 (10.5–11.3) | 10.8 (10.5–11.1) | ||||
| τ2 = 100 s | 102.7 (107.5–97.1) | 116.0 (80.5–151.5) | ||||
| 1000 | 100 | Variable | a1 = 0.75 | 0.76 (0.72–0.80) | 0.73 (0.67–0.81) | 0.9951/0.9950 |
| τ1 = 10 s | 9.5 (8.3–10.7) | 10.4 (10.1–12.8) | ||||
| τ2 = 100 s | 102.7 (85.7–119.7) | 124.8 (88.3–161.4) | ||||
| 1000 | 10 | Variable | a1 = 0.75 | 0.76 (0.72–0.80) | 0.76 (0.72–0.80) | 0.9999/0.9998 |
| τ1 = 10 s | 9.5 (8.3–10.7) | 11.08 (10.6–11.6) | ||||
| τ2 = 100 s | 102.7 (85.7–119.7) | 114.4 (60.9–167.9) | ||||
| 100 | 10 | Variable | a1 = 0.75 | 0.79 (0.59–0.99) | 0.68 (0.72–1.00) | 0.9988/0.9982 |
| τ1 = 10 s | 8.9 (3.3–14.5) | 6.9 (9.8–14.1) | ||||
| τ2 = 100 s | 90.7 (17.2–193.2) | 50.0 (−3.9 to 103.9) |
*
Intervals for each fitting method are shown in parentheses.
**
Maximum likelihood fitting results obtained using MEMLET software [34]. MEMLET is more efficient at processing large data sets (≥10000 data points) than AGATHA software.