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Figure from:A generalization of Ramos-Louzada distribution: Properties and estimation

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Table 1. Mean, variance, skewness and kurtosis of the GRL distribution for different values of the parameters A and a

Table 1 Mean, variance, skewness and kurtosis of the GRL distribution for different values of the parameters A and a

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Figure 1. PDF shapes for the GRL distribution considering different values of A and a.
Figure 1. PDF shapes for the GRL distribution considering different values of A and a.
Figure 2. Hazard rat function shapes for the GRL considering different values of A and a. The GRL distribution can be expressed as a two-component mixture
Figure 2. Hazard rat function shapes for the GRL considering different values of A and a. The GRL distribution can be expressed as a two-component mixture
Proposition 3. The r—th central moment for the GRL distribution is given by
Proposition 3. The r—th central moment for the GRL distribution is given by
where the elements of the observed Fisher information matrix H(A,«) are given by with respect to A and w. Or equivalently, the OLSEs follow by solving the non-linear equations From the expressions al (g;t) =0, 21 (p;t) = 0, we get the likelihood equations
where the elements of the observed Fisher information matrix H(A,«) are given by with respect to A and w. Or equivalently, the OLSEs follow by solving the non-linear equations From the expressions al (g;t) =0, 21 (p;t) = 0, we get the likelihood equations
Table 12. Goodness-of-fit statistics, MLEs and SEs for leukaemia data
Table 12. Goodness-of-fit statistics, MLEs and SEs for leukaemia data
Table 13. Goodness-of-fit statistics, MLEs and SEs for epicenter data
Table 13. Goodness-of-fit statistics, MLEs and SEs for epicenter data
Table 14. The parameter estimates under various estimation methods and the goodness-of-fit statistics for leukaemia data
Table 14. The parameter estimates under various estimation methods and the goodness-of-fit statistics for leukaemia data
Figure 3. PDFs and CDFs of the fitted models for leukaemia data
Figure 3. PDFs and CDFs of the fitted models for leukaemia data
Table 15. The parameter estimates under various estimation methods and the goodness-of-fit statistics for epicenter data
Table 15. The parameter estimates under various estimation methods and the goodness-of-fit statistics for epicenter data
Figure 5. The HRF plot of the GRL distribution and TTT plot for leukaemia date
Figure 5. The HRF plot of the GRL distribution and TTT plot for leukaemia date
Figure 6. The HRF plot of the GRL distribution and TTT plot for epicenter data
Figure 6. The HRF plot of the GRL distribution and TTT plot for epicenter data
Table 2. Simulation results for @ = (A = 2.0,a = 0.5)T
Table 2. Simulation results for @ = (A = 2.0,a = 0.5)T
Table 5. Simulation results for @ = (A = 2.0,a = 3.5)T
Table 5. Simulation results for @ = (A = 2.0,a = 3.5)T
Table 9. Simulation results for @ = (A = 3.1,a = 3.5)T
Table 9. Simulation results for @ = (A = 3.1,a = 3.5)T