Table 3.
Parameter and goodness-of-fit estimates of 10 distributions fitted to four data sets
| Dataset (size) | Distribution | Parameter (SE) | AIC|BIC | |||
|---|---|---|---|---|---|---|
| ADHD (n = 3360) | EXP | 3.105 (0.054) | NA (NA) | NA (NA) | NA (NA) | 14335.086|14341.205 |
| NO | 3.105 (0.021) | 1.231 (0.015) | NA (NA) | NA (NA) | 10936.058|10948.298 | |
| T | 2.831 (0.013) | 0.584 (0.011) | 2.449 (0.096) | NA (NA) | 8872.626|8890.985 | |
| EG | 2.109 (0.010) | 0.264 (0.010) | 0.996 (0.015) | NA (NA) | 8215.94|8234.30 | |
| G | 3.105 (0.017) | 0.316 (0.004) | NA (NA) | NA (NA) | 9171.67|9183.91 | |
| LN | 2.951 (0.015) | 0.297 (0.004) | NA (NA) | NA (NA) | 8652.98|8665.22 | |
| SNAP | 3.061 (0.043) | 2.943 (0.008) | 15.521 (0.913) | 0.120 (0.081) | 8379.29|8403.77 | |
| SN | 2.02 (0.009) | 0.516 (0.002) | 3.321 (0.012) | NA (NA) | 9077.44v9095.80 | |
| ECSN | 1.856 (0.056) | 0.387 (0.054) | 1.015 (0.024) | 1.634 (0.611) | 8215.42|8239.90 | |
| GEG | 2.471 (0.078) | 0.253 (0.009) | 0.835 (0.044) | 0.486 (0.074) | 8197.86|8222.34 | |
| M.S (n = 3980) | EXP | 2.371 (0.038) | NA (NA) | NA (NA) | NA (NA) | 14832.983|14839.272 |
| NO | 2.371 (0.01) | 0.631 (0.007) | NA (NA) | NA (NA) | 7632.219|7644.798 | |
| T | 2.263 (0.004) | 0.198 (0.003) | 2.029 (0.066) | NA (NA) | 2650.054|2668.921 | |
| EG | 2.012 (0.005) | 0.191 (0.002) | 0.358 (0.003) | NA (NA) | 3290.43|3309.29 | |
| G | 2.371 (0.008) | 0.201 (0.002) | NA (NA) | NA (NA) | 5273.32|5285.89 | |
| LN | 2.323 (0.007) | 0.183 (0.002) | NA (NA) | NA (NA) | 4499.72|4512.30 | |
| SNAP | − 17.444 (NaN) | 2.694 (0.004) | 37.56 (0.021) | 3104014918865.67 (NaN) | 4170.55|4195.70 | |
| SN | 2.053 (0.006) | 0.398 (0.001) | 1.974 (0.004) | NA (NA) | 5669.91|5688.78 | |
| ECSN | 2.013 (NaN) | 0.191 (0.004) | 2.79 (0.059) | − 0.002 (NaN) | 3292.42|3317.58 | |
| GEG | 2.503 (0.011) | 0.071 (0.002) | 0.807 (0.065) | 0.061 (0.005) | 2546.67|2571.83 | |
| C.D. (n = 162) | EXP | 1.684 (0.132) | NA (NA) | NA (NA) | NA (NA) | 494.874|497.962 |
| NO | 1.684 (0.058) | 0.737 (0.041) | NA (NA) | NA (NA) | 364.894|371.069 | |
| T | 1.6 (0.056) | 0.644 (0.042) | 7.818 (3.184) | NA (NA) | 365.753|375.016 | |
| EG | 0.901 (0.031) | 0.164 (0.040) | 0.783 (0.069) | NA (NA) | 309.08|318.34 | |
| G | 1.684 (0.054) | 0.411 (0.022) | NA (NA) | NA (NA) | 325.43|331.61 | |
| LN | 1.544 (0.050) | 0.410 (0.023) | NA (NA) | NA (NA) | 315.55|321.72 | |
| SNAP | 1.102 (0.133) | 1.282 (0.038) | 8.929 (1.792) | 0.459 (1.653) | 306.89|319.24 | |
| SN | 0.893 (0.028) | 0.350 (0.019) | 3.235 (0.165) | NA (NA) | 310.58|319.84 | |
| ECSN | 0.651 (0.028) | 0.331 (0.080) | 1.302 (0.136) | 354.056 (11863.415) | 308.53|320.88 | |
| GEG | 0.663 (0.038) | 0.003 (4.123) | 1.447 (0.143) | 1.946 (0.361) | 308.76|321.11 | |
| S.S.N. (n = 171) | EXP | 0.144 (0.011) | NA (NA) | NA (NA) | NA (NA) | − 319.179|− 316.038 |
| NO | 0.144 (0.004) | 0.047 (0.003) | NA (NA) | NA (NA) | − 553.518|− 547.234 | |
| T | 0.143 (0.004) | 0.046 (0.003) | 27.098 (31.564) | NA (NA) | − 551.764|− 542.339 | |
| EG | 0.102 (0.003) | 0.027 (0.005) | 0.042 (0.004) | NA (NA) | − 565.531|− 556.106 | |
| G | 0.144 (0.004) | 0.324 (0.017) | NA (NA) | NA (NA) | − 572.003|− 565.719 | |
| LN | 0.136 (0.003) | 0.327 (0.018) | NA (NA) | NA (NA) | − 573.931|− 567.648 | |
| SNAP | − 1.166 (1.508) | 0.686 (0.353) | − 2.818 (3.024) | 2162326935.754 (43972887567.382) | − 568.638|− 556.071 | |
| SN | 0.085 (0.002) | 0.025 (0.002) | 3.162 (0.178) | NA (NA) | − 580.824|− 571.399 | |
| ECSN | 0.103 (0.128) | 0.028 (0.004) | 24.38 (3.841) | − 0.006 (5.82) | − 563.553|− 550.986 | |
| GEG | 0.063 (0.008) | 0.002 (0.035) | 21.475 (2.345) | 2.716 (1.041) | − 572.157|− 559.59 | |
The number of parameters of each distribution is shown in brackets. EXP = Exponential (1), NO = Normal (2), T = t-distribution (3), EG = Ex-Gaussian (3), G = Gamma (2), LN = Log-Normal (2), SNAP = Skew-Normal Alpha-Power (4), SN = Skew-Normal (3), ECSN = Exponential-Centred Skew-Normal (4), GEG = Generalised Exponential Gaussian (4). The sample size of each data set (n) is shown in brackets. ADHD = simple RTs of participants with ADHD (RTs correspond to several trials from several ADHD participants; no RTs discarded), M.S = reaching RTs of monkey S to a visual target presented on the right side under a normal viewing condition (RTs are from several trials across several sessions; RTs > 50 ms were retained), C.D = neuronal RTs of an adult carrion crow during a visual task, and S.S.N. = response latencies of synchronised state neurons (synchronised state was defined as oscillations of high amplitude and low frequency (<4 Hz)). Lowest AIC|BIC estimates are shown in bold. SE = standard error. Note the SNAP distribution gave biased estimates in the M.S. and S.S.N. data sets, and the ECSN distribution gave biased estimates in the M.S., C.D., and S.S.N. data sets. These situations reflect difficulties with convergence in numerical optimisation of the MLEs