Research Article
T-Dagum: A Way of Generalizing Dagum Distribution Using Lomax Quantile Function
Table 1
Simulation results of MLE.
| Parameter | | Estimate | SE | AAB | RMSE |
| α = 1.5 | 20 | 1.5020 | 0.0000549 | 0.001610 | 0.00720 | 50 | 1.5013 | 0.0000204 | 0.000660 | 0.00466 | 100 | 1.5017 | 0.0000132 | 0.000360 | 0.00357 | 250 | 1.5020 | 0.0000032 | 0.000120 | 0.00184 | 500 | 1.5001 | 0.0000001 | 0.000010 | 0.00010 |
| β = 0.1 | 20 | 0.0367 | 1.0443120 | 0.222721 | 0.99604 | 50 | 0.1447 | 0.3889741 | 0.087315 | 0.61741 | 100 | 0.1437 | 0.1935787 | 0.043777 | 0.43777 | 250 | 0.1596 | 0.0765768 | 0.017467 | 0.27617 | 500 | 0.4500 | 0.0002455 | 0.000700 | 0.01565 |
| γ = 2.0 | 20 | 2.0110 | 0.0142591 | 0.026025 | 0.11639 | 50 | 2.0111 | 0.0053693 | 0.010259 | 0.07254 | 100 | 2.0013 | 0.0026316 | 0.005104 | 0.05104 | 250 | 2.0010 | 0.0010761 | 0.002071 | 0.03274 | 500 | 2.0001 | 0.0005010 | 0.001000 | 0.02236 |
| ϕ = 0.3 | 20 | 0.3015 | 0.3286991 | 0.124953 | 0.55881 | 50 | 0.3012 | 0.1237652 | 0.049252 | 0.34827 | 100 | 0.3011 | 0.0626044 | 0.024895 | 0.24895 | 250 | 0.2996 | 0.0246000 | 0.009900 | 0.15653 | 500 | 0.2999 | 0.0001804 | 0.000600 | 0.01342 |
| q = 0.01 | 20 | 0.0002 | 0.0624754 | 0.054476 | 0.24362 | 50 | 0.0154 | 0.0241751 | 0.021768 | 0.15392 | 100 | 0.0130 | 0.0119727 | 0.010887 | 0.10887 | 250 | 0.0116 | 0.0047506 | 0.004350 | 0.06879 | 500 | 0.0101 | 0.0000000 | 0.000000 | 0.00000 |
| u = 0.9 | 20 | 0.9014 | 0.0000152 | 0.000849 | 0.00379 | 50 | 0.9008 | 0.0000052 | 0.000319 | 0.00226 | 100 | 0.9005 | 0.0000021 | 0.000144 | 0.00144 | 250 | 0.9002 | 0.0000012 | 0.000070 | 0.00111 | 500 | 0.9001 | 0.0000010 | 0.000001 | 0.00000 |
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