If we study the results of the tables (2 and 3), in which sample sizes are (40, and 150) and the combinations of the values of (β, γ) = {(1, 2), (2, 1) and (1.5, 1.5)}. Then we get the results that MLM is the best for the estimation of β and γ. After MLM, the P.E is best for the estimation of scale and shape parameters of the BL2PFD.
Application and Discussion
In this section, we have analyzed two real life data sets to demonstrate the performance of BL2PFD. The comparison of the Probability distributions has been made in all the data sets on the basis of Akaike information criterion (AIC), the correct Akaike information criterion (CAIC), Bayesian information criterion (BIC) and Hannan-Quinn information criterion (HQIC).
Finally, using the above mentioned criteria’s, our proposed BL2PFD is better than the different competitor models for the same data sets.
Bladder Cancer Data
We have adopted the data set consisting the remission time of 128 bladder cancer patients to demonstrate the performance of our proposed BL2PFD. These data were also studied by [23] and [24]. The remission times in months are given: 0.08, 0.20, 0.40, 0.50, 0.51, 0.81, 0.90, 1.05, 1.19, 1.26, 1.35, 1.40, 1.46, 1.76, 2.02, 2.02, 2.07, 2.09, 2.23, 2.26, 2.46, 2.54, 2.62, 2.64, 2.69, 2.69, 2.75, 2.83, 2.87, 3.02, 3.25, 3.31, 3.36, 3.36, 3.48, 3.52, 3.57, 3.64, 3.70, 3.82, 3.88, 4.18, 4.23, 4.26, 4.33, 4.34, 4.40, 4.50, 4.51, 4.87, 4.98, 5.06, 5.09, 5.17, 5.32, 5.32, 5.34, 5.41, 5.41, 5.49, 5.62, 5.71, 5.85, 6.25, 6.54, 6.76, 6.93, 6.94, 6.97, 7.09, 7.26, 7.28, 7.32, 7.39, 7.59, 7.62, 7.63, 7.66, 7.87, 7.93, 8.26, 8.37, 8.53, 8.65, 8.66, 9.02, 9.22, 9.47, 9.74, 10.06, 10.34, 10.66, 10.75, 11.25, 11.64, 11.79, 11.98, 12.02, 12.03, 12.07, 12.63, 13.11, 13.29, 13.80, 14.24, 14.76, 14.77, 14.83, 15.96, 16.62, 17.12, 17.14, 17.36, 18.10, 19.13, 20.28, 21.73, 22.69, 23.63, 25.74, 25.82, 26.31, 32.15, 34.26, 36.66, 43.01,46.12 ,79.05.
We have compared our proposed BL2PFD with the Beta Exponentiated Pareto distribution (BEPD) by McDonald‘s Power function distribution (McPFD) by [14], Kumaraswamy Power function distribution (KPFD) by [15], Beta exponentiated Pareto (BEPD) by [23], Marshall-Olkin Power Lomax distribution (MOPLx) by [25], and Power function distribution (PFD).