Exploring the Dynamics of COVID-19 with a Novel Family of Models
Abstract
:1. Introduction
2. The New Family of Distributions
2.1. Asymptotics
2.2. Useful Representation
2.3. Order Statistics (OS)
2.4. Entropy
2.4.1. Rényi Entropy
2.4.2. Tsallis Entropy
2.4.3. Havrda and Charvat Entropy
2.5. Inference
3. Mathematical Characteristics of Sub-Model
3.1. Useful Representation
3.2. Moments and Related Measures
3.3. Residuals and Related Measures
3.3.1. Mean Residual and Mean Inactivity Time
3.4. Entropy
3.4.1. Rényi Entropy
3.4.2. Tsallis Entropy
3.4.3. Havrda and Charvat Entropy
3.5. Order Statistics (OS)
4. Inference
4.1. Maximum Likelihood Estimation Method (MLE)
4.2. Anderson–Darling Estimation Method (ADE-M)
4.3. Cram’er–Von Mises Estimation Method (CVME-M)
4.4. Least Squares Estimation Method (LSE-M)
4.5. Weighted Least-Squares Estimation Method (WLSE-M)
4.6. Maximum Product of Spacings Estimation Method (MPSE-M)
5. Simulation Study
- We set the beginning values for the parameters of our suggested model.
- From our suggested model, we have produced random data sets using the inverse of cdf.
- Use several estimate techniques to find estimators for our proposed model.
- Calculate the bias, MSE, and MRE for each estimator using each estimating technique.
- Repeat steps 1 through 4, 500 times.
6. Analysis of COVID-19 Data
7. Summary and Conclusions
8. Future Recommendations
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Appendix A
- Application I: United Kingdom COVID-19 Mortality Rate
- Application II: Europe COVID-19 Mortality Rate
- Application III: China COVID-19 Mortality Rate
- Application IV: United Kingdom COVID-19 Mortality Rate
- Application V: Nepal COVID-19 Mortality Rate
- Application VI: Netherland COVID-19 Mortality Rate
- Application VII: Italy COVID-19 Mortality Rate
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Model | Base Model | New Model |
---|---|---|
Exponential | ||
Weibull | ||
Rayleigh | ||
Gompertz | ||
Lomax | ||
Burr | ||
Pareto | ||
Half Log-Logistic | ||
Kumaraswamy | ||
Power Function | ||
Uniform |
Est. | Par. | MLE-M | ADE-M | CVME-M | MPSE-M | LSE-M | WLSE-M | |
---|---|---|---|---|---|---|---|---|
20 | BIAS | 0.3769 | 0.3296 | 0.3288 | 0.3120 | 0.3697 | 0.3932 | |
0.3723 | 0.3683 | 0.3915 | 0.3293 | 0.3241 | 0.4479 | |||
MSE | 0.2035 | 0.1671 | 0.1498 | 0.1352 | 0.1689 | 0.1946 | ||
0.2903 | 0.2374 | 0.3020 | 0.1866 | 0.1949 | 0.4083 | |||
MRE | 0.7538 | 0.6593 | 0.6576 | 0.6240 | 0.7394 | 0.7864 | ||
0.2482 | 0.2455 | 0.2610 | 0.2196 | 0.2161 | 0.2986 | |||
40 | BIAS | 0.3226 | 0.3177 | 0.2933 | 0.2955 | 0.3218 | 0.3115 | |
0.2652 | 0.2654 | 0.2669 | 0.2128 | 0.2719 | 0.2403 | |||
MSE | 0.1698 | 0.1469 | 0.1170 | 0.1294 | 0.1392 | 0.1394 | ||
0.1128 | 0.1173 | 0.1192 | 0.0843 | 0.1251 | 0.1109 | |||
MRE | 0.6451 | 0.6354 | 0.5865 | 0.5910 | 0.6435 | 0.6229 | ||
0.1768 | 0.1770 | 0.1780 | 0.1419 | 0.1813 | 0.1602 | |||
80 | BIAS | 0.2865 | 0.2372 | 0.2258 | 0.2450 | 0.2577 | 0.2499 | |
0.1836 | 0.1790 | 0.1891 | 0.1689 | 0.1741 | 0.1767 | |||
MSE | 0.1457 | 0.0925 | 0.0828 | 0.0998 | 0.1098 | 0.1059 | ||
0.0632 | 0.0521 | 0.0550 | 0.0538 | 0.0547 | 0.0535 | |||
MRE | 0.5730 | 0.4744 | 0.4516 | 0.4901 | 0.5154 | 0.4999 | ||
0.1224 | 0.1193 | 0.1261 | 0.1126 | 0.1161 | 0.1178 | |||
100 | BIAS | 0.2538 | 0.2231 | 0.2604 | 0.2140 | 0.2631 | 0.2727 | |
0.1768 | 0.1661 | 0.1741 | 0.1501 | 0.1812 | 0.1577 | |||
MSE | 0.1142 | 0.0816 | 0.1062 | 0.0832 | 0.1109 | 0.1151 | ||
0.0556 | 0.0482 | 0.0519 | 0.0413 | 0.0528 | 0.0449 | |||
MRE | 0.5076 | 0.4462 | 0.5207 | 0.4279 | 0.5262 | 0.5455 | ||
0.1178 | 0.1107 | 0.1161 | 0.1001 | 0.1208 | 0.1051 | |||
150 | BIAS | 0.2357 | 0.2039 | 0.2321 | 0.2295 | 0.2092 | 0.2634 | |
0.1523 | 0.1357 | 0.1600 | 0.1158 | 0.1319 | 0.1414 | |||
MSE | 0.1210 | 0.0779 | 0.0974 | 0.1005 | 0.0906 | 0.1184 | ||
0.0479 | 0.0300 | 0.0528 | 0.0248 | 0.0431 | 0.0302 | |||
MRE | 0.4713 | 0.4078 | 0.4641 | 0.4590 | 0.4183 | 0.5269 | ||
0.1015 | 0.0905 | 0.1067 | 0.0772 | 0.0879 | 0.0942 | |||
200 | BIAS | 0.2177 | 0.1687 | 0.2269 | 0.1551 | 0.2126 | 0.2236 | |
0.1270 | 0.1073 | 0.1115 | 0.0926 | 0.1097 | 0.1222 | |||
MSE | 0.1030 | 0.0600 | 0.0978 | 0.0514 | 0.0872 | 0.0980 | ||
0.0273 | 0.0193 | 0.0217 | 0.0159 | 0.0200 | 0.0248 | |||
MRE | 0.4353 | 0.3375 | 0.4538 | 0.3101 | 0.4251 | 0.4472 | ||
0.0847 | 0.0715 | 0.0743 | 0.0617 | 0.0731 | 0.0815 |
Est. | Par. | MLE-M | ADE-M | CVME-M | MPSE-M | LSE-M | WLSE-M | |
---|---|---|---|---|---|---|---|---|
20 | BIAS | 0.4524 | 0.3208 | 0.3965 | 0.2681 | 0.3433 | 0.3426 | |
0.1327 | 0.1265 | 0.1600 | 0.1030 | 0.1352 | 0.1349 | |||
MSE | 0.2718 | 0.1350 | 0.1910 | 0.1034 | 0.1455 | 0.1650 | ||
0.0383 | 0.0277 | 0.0426 | 0.0238 | 0.0330 | 0.0374 | |||
MRE | 0.6032 | 0.4278 | 0.5287 | 0.3575 | 0.4577 | 0.4568 | ||
0.2655 | 0.2529 | 0.3199 | 0.2060 | 0.2705 | 0.2698 | |||
40 | BIAS | 0.3773 | 0.2905 | 0.3601 | 0.2529 | 0.3060 | 0.3293 | |
0.0824 | 0.0786 | 0.1078 | 0.0616 | 0.0942 | 0.0795 | |||
MSE | 0.2131 | 0.1143 | 0.1548 | 0.1018 | 0.1112 | 0.1374 | ||
0.0141 | 0.0115 | 0.0183 | 0.0083 | 0.0152 | 0.0106 | |||
MRE | 0.5031 | 0.3873 | 0.4802 | 0.3372 | 0.4080 | 0.4390 | ||
0.1649 | 0.1572 | 0.2157 | 0.1231 | 0.1884 | 0.1590 | |||
80 | BIAS | 0.2763 | 0.2139 | 0.3093 | 0.2312 | 0.2794 | 0.2613 | |
0.0497 | 0.0542 | 0.0661 | 0.0419 | 0.0647 | 0.0602 | |||
MSE | 0.1272 | 0.0754 | 0.1120 | 0.0938 | 0.0978 | 0.0858 | ||
0.0053 | 0.0061 | 0.0081 | 0.0035 | 0.0078 | 0.0062 | |||
MRE | 0.3684 | 0.2852 | 0.4125 | 0.3083 | 0.3725 | 0.3484 | ||
0.0993 | 0.1084 | 0.1321 | 0.0838 | 0.1293 | 0.1203 | |||
100 | BIAS | 0.2598 | 0.1988 | 0.2691 | 0.1739 | 0.2452 | 0.2783 | |
0.0428 | 0.0445 | 0.0514 | 0.0311 | 0.0547 | 0.0606 | |||
MSE | 0.1216 | 0.0647 | 0.0946 | 0.0633 | 0.0823 | 0.0992 | ||
0.0045 | 0.0043 | 0.0045 | 0.0024 | 0.0047 | 0.0065 | |||
MRE | 0.3464 | 0.2650 | 0.3589 | 0.2318 | 0.3270 | 0.3711 | ||
0.0856 | 0.0890 | 0.1028 | 0.0623 | 0.1094 | 0.1212 | |||
150 | BIAS | 0.2659 | 0.1839 | 0.2481 | 0.1731 | 0.2767 | 0.2420 | |
0.0446 | 0.0318 | 0.0465 | 0.0334 | 0.0446 | 0.0439 | |||
MSE | 0.1286 | 0.0632 | 0.0792 | 0.0642 | 0.0901 | 0.0779 | ||
0.0046 | 0.0022 | 0.0035 | 0.0027 | 0.0033 | 0.0031 | |||
MRE | 0.3546 | 0.2453 | 0.3307 | 0.2308 | 0.3690 | 0.3227 | ||
0.0893 | 0.0636 | 0.0930 | 0.0668 | 0.0891 | 0.0879 | |||
200 | BIAS | 0.2047 | 0.1354 | 0.2469 | 0.1375 | 0.2556 | 0.2536 | |
0.0317 | 0.0268 | 0.0484 | 0.0223 | 0.0428 | 0.0427 | |||
MSE | 0.0950 | 0.0386 | 0.0761 | 0.0481 | 0.0814 | 0.0781 | ||
0.0030 | 0.0018 | 0.0037 | 0.0013 | 0.0029 | 0.0032 | |||
MRE | 0.2730 | 0.1805 | 0.3292 | 0.1833 | 0.3408 | 0.3381 | ||
0.0633 | 0.0536 | 0.0967 | 0.0446 | 0.0856 | 0.0854 |
Est. | Par. | MLE-M | ADE-M | CVME-M | MPSE-M | LSE-M | WLSE-M | |
---|---|---|---|---|---|---|---|---|
20 | BIAS | 1.1442 | 0.2833 | 0.3719 | 0.3823 | 0.4131 | 0.3160 | |
0.1602 | 0.1293 | 0.1434 | 0.1475 | 0.1504 | 0.1414 | |||
MSE | 1.6432 | 0.1557 | 0.2312 | 0.2903 | 0.2905 | 0.1607 | ||
0.0408 | 0.0307 | 0.0316 | 0.0331 | 0.0361 | 0.0305 | |||
MRE | 0.4577 | 0.1133 | 0.1488 | 0.1529 | 0.1653 | 0.1264 | ||
0.2136 | 0.1724 | 0.1912 | 0.1967 | 0.2005 | 0.1885 | |||
40 | BIAS | 0.8187 | 0.1869 | 0.3060 | 0.2338 | 0.3459 | 0.2289 | |
0.1534 | 0.0950 | 0.1106 | 0.0853 | 0.1104 | 0.1052 | |||
MSE | 1.1100 | 0.0648 | 0.1467 | 0.1348 | 0.2198 | 0.0965 | ||
0.0428 | 0.0135 | 0.0195 | 0.0115 | 0.0204 | 0.0181 | |||
MRE | 0.3275 | 0.0747 | 0.1224 | 0.0935 | 0.1384 | 0.0916 | ||
0.2045 | 0.1267 | 0.1474 | 0.1138 | 0.1473 | 0.1402 | |||
80 | BIAS | 0.5424 | 0.1206 | 0.1838 | 0.1014 | 0.1968 | 0.1544 | |
0.1142 | 0.0673 | 0.0815 | 0.0586 | 0.0770 | 0.0759 | |||
MSE | 0.6064 | 0.0286 | 0.0564 | 0.0168 | 0.0653 | 0.0417 | ||
0.0250 | 0.0072 | 0.0104 | 0.0057 | 0.0090 | 0.0082 | |||
MRE | 0.2170 | 0.0483 | 0.0735 | 0.0406 | 0.0787 | 0.0618 | ||
0.1523 | 0.0897 | 0.1087 | 0.0781 | 0.1027 | 0.1012 | |||
100 | BIAS | 0.5402 | 0.0992 | 0.1572 | 0.0818 | 0.1865 | 0.1131 | |
0.1370 | 0.0632 | 0.0556 | 0.0457 | 0.0674 | 0.0526 | |||
MSE | 0.5514 | 0.0184 | 0.0420 | 0.0111 | 0.0506 | 0.0200 | ||
0.0362 | 0.0064 | 0.0051 | 0.0037 | 0.0075 | 0.0046 | |||
MRE | 0.2161 | 0.0397 | 0.0629 | 0.0327 | 0.0746 | 0.0452 | ||
0.1826 | 0.0843 | 0.0741 | 0.0609 | 0.0898 | 0.0702 | |||
150 | BIAS | 0.3914 | 0.0701 | 0.1261 | 0.0587 | 0.1387 | 0.0879 | |
0.0915 | 0.0393 | 0.0524 | 0.0397 | 0.0517 | 0.0486 | |||
MSE | 0.3582 | 0.0099 | 0.0252 | 0.0066 | 0.0318 | 0.0118 | ||
0.0172 | 0.0025 | 0.0043 | 0.0026 | 0.0040 | 0.0038 | |||
MRE | 0.1566 | 0.0281 | 0.0504 | 0.0235 | 0.0555 | 0.0352 | ||
0.1221 | 0.0523 | 0.0699 | 0.0530 | 0.0690 | 0.0648 | |||
200 | BIAS | 0.2187 | 0.0536 | 0.1108 | 0.0354 | 0.1192 | 0.0755 | |
0.0579 | 0.0378 | 0.0487 | 0.0299 | 0.0453 | 0.0406 | |||
MSE | 0.0880 | 0.0064 | 0.0195 | 0.0022 | 0.0225 | 0.0082 | ||
0.0068 | 0.0025 | 0.0035 | 0.0017 | 0.0031 | 0.0027 | |||
MRE | 0.0875 | 0.0215 | 0.0443 | 0.0142 | 0.0477 | 0.0302 | ||
0.0772 | 0.0504 | 0.0649 | 0.0398 | 0.0604 | 0.0542 |
Est. | Par. | MLE-M | ADE-M | CVME-M | MPSE-M | LSE-M | WLSE-M | |
---|---|---|---|---|---|---|---|---|
20 | BIAS | 0.6551 | 0.5539 | 0.5667 | 0.5194 | 0.5117 | 0.5046 | |
0.5853 | 0.5147 | 0.5672 | 0.5333 | 0.5370 | 0.5565 | |||
MSE | 0.8185 | 0.4264 | 0.4388 | 0.3312 | 0.3496 | 0.3353 | ||
0.5296 | 0.4334 | 0.5226 | 0.3938 | 0.4555 | 0.4805 | |||
MRE | 0.4367 | 0.3693 | 0.3778 | 0.3463 | 0.3411 | 0.3364 | ||
0.2341 | 0.2059 | 0.2269 | 0.2133 | 0.2148 | 0.2226 | |||
40 | BIAS | 0.4699 | 0.4312 | 0.4480 | 0.4797 | 0.4561 | 0.4303 | |
0.4674 | 0.4015 | 0.4695 | 0.4247 | 0.3905 | 0.4035 | |||
MSE | 0.2956 | 0.2428 | 0.2840 | 0.3135 | 0.2724 | 0.2252 | ||
0.3515 | 0.2245 | 0.3717 | 0.2447 | 0.2339 | 0.2738 | |||
MRE | 0.3133 | 0.2875 | 0.2987 | 0.3198 | 0.3041 | 0.2869 | ||
0.1870 | 0.1606 | 0.1878 | 0.1699 | 0.1562 | 0.1614 | |||
80 | BIAS | 0.3615 | 0.3707 | 0.3991 | 0.3688 | 0.3920 | 0.3369 | |
0.3561 | 0.2647 | 0.3746 | 0.3453 | 0.3465 | 0.2991 | |||
MSE | 0.1906 | 0.1830 | 0.2170 | 0.1995 | 0.2006 | 0.1527 | ||
0.1944 | 0.1216 | 0.2243 | 0.1818 | 0.1802 | 0.1374 | |||
MRE | 0.2410 | 0.2471 | 0.2661 | 0.2459 | 0.2613 | 0.2246 | ||
0.1424 | 0.1059 | 0.1498 | 0.1381 | 0.1386 | 0.1197 | |||
100 | BIAS | 0.3808 | 0.3453 | 0.3706 | 0.4104 | 0.3278 | 0.3254 | |
0.3515 | 0.2927 | 0.3085 | 0.3352 | 0.2728 | 0.2765 | |||
MSE | 0.1986 | 0.1607 | 0.1639 | 0.2329 | 0.1525 | 0.1499 | ||
0.1995 | 0.1271 | 0.1579 | 0.1677 | 0.1200 | 0.1195 | |||
MRE | 0.2539 | 0.2302 | 0.2470 | 0.2736 | 0.2185 | 0.2170 | ||
0.1406 | 0.1171 | 0.1234 | 0.1341 | 0.1091 | 0.1106 | |||
150 | BIAS | 0.2997 | 0.2534 | 0.3034 | 0.3213 | 0.3070 | 0.3110 | |
0.2417 | 0.2349 | 0.2779 | 0.2508 | 0.2770 | 0.2720 | |||
MSE | 0.1447 | 0.1010 | 0.1283 | 0.1701 | 0.1295 | 0.1376 | ||
0.0890 | 0.0881 | 0.1206 | 0.0988 | 0.1082 | 0.1020 | |||
MRE | 0.1998 | 0.1689 | 0.2023 | 0.2142 | 0.2047 | 0.2073 | ||
0.0967 | 0.0940 | 0.1112 | 0.1003 | 0.1108 | 0.1088 | |||
200 | BIAS | 0.2640 | 0.2652 | 0.3074 | 0.3507 | 0.2594 | 0.2394 | |
0.2121 | 0.2225 | 0.2266 | 0.2427 | 0.2349 | 0.2063 | |||
MSE | 0.1234 | 0.1032 | 0.1193 | 0.1943 | 0.0987 | 0.0902 | ||
0.0762 | 0.0796 | 0.0746 | 0.0966 | 0.0821 | 0.0654 | |||
MRE | 0.1760 | 0.1768 | 0.2050 | 0.2338 | 0.1729 | 0.1596 | ||
0.0848 | 0.0890 | 0.0906 | 0.0971 | 0.0940 | 0.0825 |
Model | Estimates | Fitted Measures | |||||||
---|---|---|---|---|---|---|---|---|---|
AIC | CVM | AD | KS | p-Value | SS | ||||
New-PFD | 0.0314 | 0.4012 | - | 283.6512 | 0.1934 | 1.2679 | 0.0777 | 0.7488 | 0.1147 |
Tr-PF | 0.7647 | - | 1.5949 | 291.6001 | 0.3140 | 1.9964 | 0.1329 | 0.1367 | 0.3548 |
Kum-PF | 1.1071 | 0.4754 | 1.3700 | 302.9045 | 0.4286 | 2.6819 | 0.1582 | 0.0446 | 0.5521 |
OGE-PF | 6.4256 | 0.0690 | 2.0309 | 309.0742 | 0.3635 | 2.3533 | 0.1959 | 0.0058 | 0.9499 |
PF-I | 0.4375 | - | - | 302.9309 | 0.4179 | 2.6213 | 0.1976 | 0.0053 | 0.9699 |
NG-PF | 0.6775 | 0.0727 | 5.8366 | 305.8946 | 0.3440 | 2.1834 | 0.0777 | 0.0038 | 1.0395 |
Gen-PF | 2.2790 | - | - | 332.1345 | 0.3500 | 2.1641 | 0.3180 | 0.0000 | 3.0369 |
Model | Estimates | Fitted Measures | |||||||
---|---|---|---|---|---|---|---|---|---|
AIC | CVM | AD | KS | p-Value | SS | ||||
New-PFD | 0.1921 | 0.3262 | - | 470.1407 | 0.1433 | 0.9490 | 0.1232 | 0.6889 | 0.0760 |
ZTP-PF | 2.8368 | 0.7329 | - | 476.5421 | - | - | 0.1728 | 0.2790 | 0.1924 |
Kum-PF | 1.2485 | 0.2696 | 0.6369 | 467.5365 | 0.1976 | 1.2621 | 0.1797 | 0.2393 | 0.2962 |
OGE-PF | 4.7180 | 0.0646 | 0.0047 | 475.6623 | 0.1195 | 0.8823 | 0.2213 | 0.0818 | 0.4595 |
Gen-PF | 1.0351 | - | - | 494.4784 | 0.1204 | 0.7690 | 0.3991 | 0.0001 | 1.8877 |
Model | Estimates | Fitted Measures | |||||||
---|---|---|---|---|---|---|---|---|---|
AIC | CVM | AD | KS | p-Value | SS | ||||
New-PFD | 0.1044 | 0.4908 | - | 642.4877 | 0.1217 | 0.8393 | 0.0814 | 0.7740 | 0.0924 |
Tr-PF | 0.5604 | - | 1.7920 | 643.7063 | 0.1588 | 1.0521 | 0.1032 | 0.4836 | 0.1446 |
NG-PF | 1.1644 | 17.2847 | 0.0531 | 648.6244 | 0.1868 | 1.2314 | 0.0814 | 0.2892 | 0.1946 |
Kum-PF | 0.3894 | 1.6505 | 1.0472 | 650.1455 | 0.2125 | 1.3840 | 0.1464 | 0.1182 | 0.2983 |
PF-I | 0.6247 | - | - | 646.2304 | 0.2118 | 1.3797 | 0.1521 | 0.0945 | 0.3314 |
Model | Estimates | Fitted Measures | |||||||
---|---|---|---|---|---|---|---|---|---|
AIC | CVM | AD | KS | p-Value | SS | ||||
New-PFD | 0.0287 | 1.3984 | - | −41.7665 | 0.0255 | 0.2089 | 0.0835 | 0.9910 | 0.0199 |
NG-PF | 1.5971 | 18.5499 | 0.2342 | −38.5436 | 0.0361 | 0.3030 | 0.0835 | 0.9651 | 0.0265 |
Kum-PF | 0.9756 | 2.1057 | 1.7528 | −36.7425 | 0.0532 | 0.4306 | 0.1276 | 0.7836 | 0.0555 |
Tr-PF | 0.8341 | - | 1.0780 | −39.9779 | 0.0382 | 0.3138 | 0.1277 | 0.7826 | 0.0522 |
PF-I | 1.4845 | - | - | −37.2526 | 0.0498 | 0.4067 | 0.2310 | 0.1311 | 0.2499 |
Estimates | Fitted Measures | ||||||||
---|---|---|---|---|---|---|---|---|---|
Model | AIC | CVM | AD | KS | p-Value | SS | |||
New-PFD | 0.0205 | 0.8481 | - | 993.5991 | 0.0471 | 0.4678 | 0.0519 | 0.8044 | 0.0531 |
W-PF | 4.2216 | 8.4898 | 0.2024 | 996.1838 | 0.0597 | 0.5134 | 0.0548 | 0.7468 | 0.0594 |
ZTP-PF | 4.3987 | 1.7816 | - | 998.4550 | 0.1012 | 0.8065 | 0.0679 | 0.4803 | 0.1028 |
MOE-PF | 0.1416 | 1.9682 | - | 994.8340 | 0.0874 | 0.7155 | 0.0681 | 0.4774 | 0.0815 |
Gen-PF | 1.7756 | - | - | 979.7377 | 0.5117 | 3.7593 | 0.0716 | 0.4132 | 0.1176 |
Kum-PF | 0.4168 | 3.0564 | 1.9823 | 1012.3107 | 0.1206 | 0.9920 | 0.0790 | 0.2948 | 0.1706 |
Tr-PF | 0.9380 | - | 1.2519 | 1002.0116 | 0.0784 | 0.6836 | 0.0819 | 0.2563 | 0.1993 |
OGE-PF | 7.6256 | 0.1239 | 2.8673 | 1035.8485 | 0.2114 | 1.5872 | 0.1621 | 0.0006 | 1.0577 |
PF-I | 0.8615 | - | - | 1039.2363 | 0.1050 | 0.8905 | 0.1992 | 0.0000 | 1.6514 |
Model | Estimates | Fitted Measures | |||||||
---|---|---|---|---|---|---|---|---|---|
AIC | CVM | AD | KS | p-Value | SS | ||||
New-PFD | 0.0253 | 0.8957 | - | 156.8105 | 0.1062 | 0.6493 | 0.1070 | 0.8467 | 0.0522 |
PF-Poi | −3.5098 | 1.7625 | - | 156.8312 | 0.1076 | 0.6575 | 0.1093 | 0.8283 | 0.0549 |
Tr-PF | 0.8025 | - | 1.3066 | 160.1585 | 0.1701 | 1.0188 | 0.1617 | 0.3725 | 0.1589 |
NG-PF | 1.3880 | 164.1245 | 0.1819 | 1.1150 | 0.1070 | 0.3563 | 0.1619 | ||
Kum-PF | 0.4400 | 2.4843 | 1.2740 | 167.1066 | 0.2316 | 1.4057 | 0.2097 | 0.1232 | 0.2811 |
OGE-PF | 9.8176 | 0.1003 | 2.8782 | 168.6015 | 0.1665 | 0.9571 | 0.2378 | 0.0562 | 0.3771 |
Model | Estimates | Fitted Measures | |||||||
---|---|---|---|---|---|---|---|---|---|
AIC | CVM | AD | KS | p-Value | SS | ||||
New-PFD | 0.0442 | 0.8961 | - | 335.7237 | 0.0979 | 0.7027 | 0.1128 | 0.4103 | 0.1011 |
Tr-PF | 0.8247 | - | 1.4090 | 338.2626 | 0.1176 | 0.8627 | 0.1162 | 0.3742 | 0.1269 |
Kum-PF | 0.5666 | 2.2183 | 1.4513 | 345.9732 | 0.1472 | 1.1037 | 0.1172 | 0.3639 | 0.1927 |
NG-PF | 1.4465 | 27.0812 | 0.0996 | 341.4392 | 0.1092 | 0.8408 | 0.1128 | 0.3496 | 0.1173 |
OGE-PF | 8.7252 | 0.1239 | 2.8958 | 349.0370 | 0.1462 | 1.0418 | 0.1414 | 0.1718 | 0.3554 |
ZTP-PF | 3.8076 | 1.9272 | - | 339.4020 | 0.1315 | 0.7659 | 0.1450 | 0.1514 | 0.1789 |
PF-I | 1.0090 | - | - | 346.1583 | 0.1420 | 1.0706 | 0.1694 | 0.0598 | 0.4853 |
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Alghamdi, A.S.; Abd El-Raouf, M.M. Exploring the Dynamics of COVID-19 with a Novel Family of Models. Mathematics 2023, 11, 1641. https://doi.org/10.3390/math11071641
Alghamdi AS, Abd El-Raouf MM. Exploring the Dynamics of COVID-19 with a Novel Family of Models. Mathematics. 2023; 11(7):1641. https://doi.org/10.3390/math11071641
Chicago/Turabian StyleAlghamdi, Abdulaziz S., and M. M. Abd El-Raouf. 2023. "Exploring the Dynamics of COVID-19 with a Novel Family of Models" Mathematics 11, no. 7: 1641. https://doi.org/10.3390/math11071641
APA StyleAlghamdi, A. S., & Abd El-Raouf, M. M. (2023). Exploring the Dynamics of COVID-19 with a Novel Family of Models. Mathematics, 11(7), 1641. https://doi.org/10.3390/math11071641