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Figure 1.
Graph of PDF of RGW distribution for different values of parameters.
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Figure 2.
Graphs CDF of RGW distribution for different values of parameters.
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Figure 3.
The reliability function of the RGW distribution.
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Figure 4.
(a) Plot of the hazard rate function of the RGW distribution. (b) Clean plot of the hazard rate function of the RGW distribution.
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Figure 5.
Plot of the cumulative hazard rate function of the RGW distribution.
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Figure 6.
Histogram of observed and fitted lines of values of the number of customers for waiting time.
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Figure 7.
P-P plot of customers for waiting time.
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Figure 8.
Empirical and fitted number of patients against remission time.
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Figure 9.
P-P plot of remission time.
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Figure 10.
MSE comparison across parameter sets for RGW simulation.
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Figure 11.
Bias comparison across parameter sets for RGW simulation.
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Models $ \alpha $ $ \beta $ $ \theta $ $ a $ $ b $ NLL AIC BIC KS (sig.) AD CVM Weibull 1.461 10.952 − − − 318.618 641.236 646.45 0.0574 (0.897) 0.4031 0.0607 Beta-W 0.724 49.484 − 3.610 10.959 316.946 641.891 652.31 0.0368 (0.999) 0.1288 0.0177 MO-W 2.219 50.575 0.016 − − 318.688 643.376 651.19 0.0478 (0.976) 0.2626 0.0295 KuW 1 0.367 47.18 5.369 81.733 317.482 644.965 657.99 0.0453 (0.987) 0.2204 0.0337 TrW 1.571 14.029 0.611 − − 317.796 641.591 649.41 0.0488(0.972) 0.2595 0.0384 RGW 1.085 8.095 0.841 − − 316.945 639.890 647.71 0.0376 (0.999) 0.1271 0.0176 Table 1.
Estimated parameters and test statistics for waiting time.
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Models $ \alpha $ $ \beta $ $ \theta $ $ a $ $ b $ NLL AIC BIC KS(Sig.) AD CVM Weibull 1.048 9.5607 − − − 414.087 832.174 837.878 0.0700 (0.557) 0.958 0.154 Beta-W 0.528 49.643 − 3.672 8.679 410.839 829.678 841.086 0.0466 (0.944) 0.297 0.045 MO-W 1.660 49.984 − − − 410.321 826.642 835.198 0.0357 (0.997) 0.186 0.019 KuW 1.000 0.335 − 4.243 48.68 411.537 833.075 847.335 0.056(0.820) 0.488 0.079 TrW 1.133 14.619 0.745 − − 411.958 829.916 838.473 0.0587(0.769) 0.560 0.088 RGW 0.786 14.302 4.082 − − 409.824 825.649 834.205 0.0344 (0.998) 0.127 0.017 Table 2.
Estimated parameters and test statistics for remission time of bladder cancer.
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Sample size Parameter True value Estimate Bias MSE 100 θ 1.5 1.954 0.454 0.257 α 2.0 2.570 0.570 0.368 β 0.8 1.199 0.399 0.169 200 θ 1.5 1.922 0.422 0.187 α 2.0 2.549 0.549 0.323 β 0.8 1.194 0.394 0.158 500 θ 1.5 1.905 0.405 0.166 α 2.0 2.551 0.551 0.311 β 0.8 1.186 0.385 0.150 Table 3.
Simulation results for Set I.
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Sample size Parameter True value Estimate Bias MSE 100 θ 2.0 1.925 −0.075 0.039 α 3.0 3.852 0.852 0.824 β 1.8 2.261 0.461 0.224 200 θ 2.0 1.900 −0.100 0.017 α 3.0 3.819 0.819 0.717 β 1.8 2.257 0.457 0.213 500 θ 2.0 1.887 −0.113 0.015 α 3.0 3.819 0.819 0.687 β 1.8 2.490 0.449 0.203 Table 4.
Simulation results for Set II.
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Sample size Parameter True value Estimate Bias MSE 100 θ 3.0 2.919 −0.0807 11.577 α 3.0 2.999 −0.0012 0.0705 β 3.0 2.940 −0.0596 0.1979 200 θ 3.0 2.912 −0.0882 4.2503 α 3.0 2.967 −0.0313 0.0396 β 3.0 2.966 −0.0338 0.1346 500 θ 3.0 3.013 0.0127 2.2105 α 3.0 2.975 −0.0246 0.0184 β 3.0 2.993 −0.0068 0.0755 Table 5.
Simulation results for Set III.
Figures
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Tables
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