15.3594         0.6953          0.3224           0.8292          0.1821
   III        0.8735          0.2709          4.0773          0.7212          0.4326           0.8675          0.2703
    IV        0.8052          0.1504          42.8622         0.6923          0.2696           0.8023          0.1506

  : Real data estimates

\[tab:addlabel\]

   Data   $ \alpha_L $   $ \alpha_U $   $ ACL_\alpha $   $ \beta_L $   $ \beta_U $   $ ACL_\beta $
  ------ -------------- -------------- ---------------- ------------- ------------- ---------------
    I        0.6545         0.9411          0.2866         0.1373        0.1902         0.0529
    II       0.5962         1.0717          0.4754         0.1376        0.2263         0.0888
   III       0.6202         1.1269          0.5067         0.2081        0.3337         0.1256
    IV       0.6126         0.9978          0.3852         0.1186        0.1822         0.0636

  : Interval estimates based on real data

\[tab:addlabel\]

![Empirical cumulative distribution function and QQ plot for the data set-I](ecdf1){width="6.5in" height="3in"}

![Empirical cumulative distribution function and QQ plot for the data set-II](ecdf2){width="6.5in" height="3in"}

![Empirical cumulative distribution function and QQ plot for the data set-III](ecdf3){width="6.5in" height="3in"}

![Empirical cumulative distribution function and QQ plot for the data set-IV](ecdf4){width="6.5in" height="3in"}

From the tabulated value of different model selection tools, -LogL, AIC, AICC, BIC, and K-S values it has been noticed that PMaD has least -LogL, AIC, AICC, BIC, and K-S. The empirical cumulative distribution function and Q-Q plots are also given in Figure 5, 6 & 7 respectively. Therefore, PMaD can be recommended as a good alternative to the existing family of Maxwell distribution. 