Table 15 Goodness-of-fit measures for the five datasets of the KAPLL distribution and other competing LL models.
From: A flexible extension of the log-logistic model with diverse failure rate shapes and applications
Distribution | AIC | CAIC | BIC | HQIC | \(W^{*}\) | \(A^{*}\) | \(-\ell\) | KS | PV |
|---|---|---|---|---|---|---|---|---|---|
Dataset 1 | |||||||||
 KAPLL | 167.85890 | 169.62360 | 176.30330 | 170.91210 | 0.01941 | 0.15087 | 78.92943 | 0.07307 | 0.98318 |
 LL | 181.41330 | 181.73760 | 184.79100 | 182.63450 | 0.21418 | 1.40722 | 88.70663 | 0.14369 | 0.38072 |
 APLL | 209.75120 | 210.07550 | 213.12890 | 210.97240 | 0.45929 | 2.73731 | 102.87560 | 0.26291 | 0.00793 |
 TLL | 424.59910 | 425.26580 | 429.66580 | 426.43110 | 0.29479 | 1.86508 | 209.29960 | 0.71682 | 0.00000 |
 APTLL | 183.39570 | 184.06230 | 188.46230 | 185.22760 | 0.21332 | 1.40194 | 88.69784 | 0.14407 | 0.37745 |
 KMOLL | 174.94480 | 176.70950 | 183.38920 | 177.99800 | 0.07693 | 0.57260 | 82.47240 | 0.10770 | 0.74232 |
 McLL | 183.85530 | 185.62000 | 192.29970 | 186.90850 | 0.19024 | 1.27427 | 86.92764 | 0.12411 | 0.56878 |
 AWLL | 176.95100 | 179.49650 | 187.08430 | 180.61490 | 0.07699 | 0.57304 | 82.47551 | 0.10770 | 0.74231 |
Dataset 2 | |||||||||
 KAPLL | 27.68430 | 28.73693 | 38.39997 | 31.89882 | 0.01775 | 0.12224 | 8.84215 | 0.04469 | 0.99961 |
 LL | 49.57993 | 49.77993 | 53.86619 | 51.26574 | 0.49694 | 2.74897 | 22.78996 | 0.15371 | 0.10187 |
 APLL | 64.63768 | 64.83768 | 68.92394 | 66.32349 | 0.73896 | 4.09825 | 30.31884 | 0.22029 | 0.00442 |
 TLL | 495.06690 | 495.47370 | 501.49630 | 497.59560 | 0.69029 | 3.77390 | 244.53350 | 0.71750 | 0.00000 |
 APTLL | 51.41486 | 51.82164 | 57.84426 | 53.94358 | 0.49183 | 2.71991 | 22.70743 | 0.14979 | 0.11834 |
 KMOLL | 28.08611 | 29.13874 | 38.80178 | 32.30064 | 0.01807 | 0.12722 | 9.04306 | 0.05363 | 0.99349 |
 McLL | 43.98007 | 45.03270 | 54.69574 | 48.19459 | 0.31606 | 1.72577 | 16.99003 | 0.18998 | 0.02118 |
 AWLL | 42.41368 | 43.91368 | 55.27249 | 47.47111 | 0.23724 | 1.30370 | 15.20684 | 0.15224 | 0.10784 |
Dataset 3 | |||||||||
 KAPLL | 345.03000 | 345.56100 | 358.92560 | 350.67260 | 0.04197 | 0.26565 | 167.51500 | 0.04633 | 0.96039 |
  LL | 360.67000 | 360.77340 | 366.22820 | 362.92700 | 0.35495 | 2.23138 | 178.33500 | 0.08032 | 0.42650 |
 APLL | 456.01840 | 456.12180 | 461.57660 | 458.27540 | 0.96857 | 5.58224 | 226.00920 | 0.23852 | 0.00000 |
 TLL | 1142.62400 | 1142.83300 | 1150.96200 | 1146.01000 | 0.55031 | 3.27610 | 568.31220 | 0.71297 | 0.00000 |
 APTLL | 362.60310 | 362.81180 | 370.94050 | 365.98860 | 0.35212 | 2.21646 | 178.30150 | 0.07881 | 0.45075 |
 KMOLL | 345.70010 | 346.23110 | 359.59570 | 351.34270 | 0.05179 | 0.31448 | 167.85010 | 0.05364 | 0.88336 |
 McLL | 345.61430 | 346.14530 | 359.50990 | 351.25690 | 0.05363 | 0.32622 | 167.80710 | 0.05591 | 0.85091 |
AWLL | 349.04620 | 349.79620 | 365.72090 | 355.81720 | 0.07612 | 0.46281 | 168.52310 | 0.06662 | 0.66640 |
Dataset 4 | |||||||||
 KAPLL | 1713.42200 | 1713.62600 | 1731.94100 | 1720.83300 | 0.05771 | 0.38980 | 851.71080 | 0.04204 | 0.66406 |
 LL | 2150.37200 | 2150.41200 | 2157.78000 | 2153.33700 | 0.07734 | 0.56860 | 1073.18600 | 0.28760 | 0.00000 |
 APLL | 2858.35800 | 2858.39800 | 2865.76500 | 2861.32200 | 0.08269 | 0.61983 | 1427.17900 | 0.44998 | 0.00000 |
 TLL | 1722.23500 | 1722.31600 | 1733.34600 | 1726.68200 | 0.15225 | 1.02731 | 858.11750 | 0.05205 | 0.39073 |
 APTLL | 1722.23500 | 1722.31600 | 1733.34600 | 1726.68200 | 0.15225 | 1.02730 | 858.11750 | 0.05205 | 0.39073 |
 KMOLL | 1713.75400 | 1713.95800 | 1732.27300 | 1721.16500 | 0.05992 | 0.40195 | 851.87690 | 0.04233 | 0.65566 |
 McLL | 1713.51900 | 1713.72300 | 1732.03800 | 1720.93000 | 0.05966 | 0.38997 | 851.75960 | 0.04248 | 0.65101 |
 AWLL | 1742.39500 | 1742.68200 | 1764.61800 | 1751.28900 | 0.31129 | 1.88895 | 865.19770 | 0.05706 | 0.28271 |
Dataset 5 | |||||||||
 KAPLL | 2350.58500 | 2350.69000 | 2372.36500 | 2359.07900 | 0.03279 | 0.35649 | 1170.29200 | 0.02575 | 0.83958 |
 LL | 2366.13600 | 2366.15700 | 2374.84800 | 2369.53400 | 0.18117 | 1.20096 | 1181.06800 | 0.03638 | 0.43104 |
 APLL | 2401.04800 | 2401.06900 | 2409.76100 | 2404.44600 | 0.63964 | 3.86817 | 1198.52400 | 0.06408 | 0.01764 |
 TLL | 5063.91900 | 5063.96100 | 5076.98800 | 5069.01600 | 0.10583 | 0.71790 | 2528.96000 | 0.68000 | 0.00000 |
 APTLL | 2368.13600 | 2368.17800 | 2381.20400 | 2373.23200 | 0.18117 | 1.20096 | 1181.06800 | 0.03638 | 0.43104 |
 KMOLL | 2382.33100 | 2382.43600 | 2404.11100 | 2390.82500 | 0.46581 | 3.34421 | 1186.16500 | 0.05880 | 0.03725 |
 McLL | 2350.65000 | 2350.75500 | 2372.43000 | 2359.14400 | 0.03321 | 0.35872 | 1170.32500 | 0.02611 | 0.82711 |
 AWLL | 2383.62600 | 2383.77400 | 2409.76300 | 2393.81900 | 0.45517 | 3.27307 | 1185.81300 | 0.05796 | 0.04171 |
