## 5 Data Analyses  
We perform two data analyses in this section to compare the performance of LBS distribution with some other well-known distributions. The first set of data under examination consists of the lifetimes of 42 individuals who were diagnosed with head and neck cancer, which had previously been used by [21]. Cancer that evolves in the mouth, throat, nose, salivary glands or other parts of the head and neck is referred to as head and neck cancer. Table 1 presents the dataset:  
It is important to mention that we eliminated data based on participants being lost to follow-up, as indicated by [21]; that is, we have omitted the censored data and considered \begin{table}
\begin{tabular}{c c c c c c} \hline
7 & 91 & 140 & 160 & 248 & 440 \\
34 & 108 & 140 & 165 & 273 & 523 \\
42 & 112 & 146 & 173 & 277 & 583 \\
63 & 129 & 149 & 176 & 297 & 594 \\
64 & 133 & 154 & 218 & 405 & 1101 \\
83 & 133 & 157 & 225 & 417 & 1146 \\
84 & 139 & 160 & 241 & 420 & 1417 \\ \hline \end{tabular}
\end{table} 
Table 1: Lifetimes of individuals who were diagnosed with Head and Neck Cancer. Figure 8: Simulated RMSEs for the estimators of \(\beta\). the remaining ones as a complete sample. Modeling the actual data by [21] (i.e., the case of censored data) is considered for future research. The second set of data under examination represents the lifetimes of 72 Cavia Porcellus (guinea pigs) injected with various doses of Mycobacterium tuberculosis, which was previously studied by [22] among others researchers. Mycobacterium tuberculosis is a bacterium that causes tuberculosis, a contagious disease that primarily affects the lungs. Table 2 displays the dataset:  
First, we estimate the MLEs, Bias, and RMSE of parameters, AIC and BIC of Exponential, Rayleigh, Weibull, BS, and LBS distributions, then depending on the considered dataset, we compute many explanatory data analysis (EDA) measurements, as well as their approximations based on the estimated model parameters. Tables 3 and 4 list the estimators of the models' parameters as well as the AIC and BIC, while Tables 5 and 6 present the outcomes of EDA measurements. Overall, when comparing these tables, one can observe that the estimated EDA measurements assuming the LBS distribution were very near to their observed counterparts which are calculated from the sample directly. Furthermore \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{\(\alpha\)} & \multicolumn{3}{c}{\(\beta\)} & \multirow{2}{*}{**AIC**} & \multirow{2}{*}{**BIC**} \\ \cline{2-2} \cline{5-8}  & **Value** & **Bias** & **RMSE** & **Value** & **Bias** & **RMSE** \\ \hline Exponential & - & - & - & 99.81944 & 0 & 9.5598 & 808.8843 & 811.1610 \\ \hline Rayleigh & - & - & - & 128.2679 & \(-\)0.7152 & 13.5447 & 818.5921 & 820.8688 \\ \hline Weibull & 1.39295 & 0.0168 & 0.0995 & 110.5393 & \(-\)2.8794 & 10.0684 & 798.2955 & 802.8488 \\ \hline BS & 0.75999 & \(-\)0.0099 & 0.0740 & 77.52778 & 0.2859 & 6.7819 & 785.8348 & 790.3881 \\ \hline LBS & 0.41460 & \(-\)0.0033 & 0.0457 & 76.01035 & 1.1905 & 6.1102 & 783.7526 & 788.3060 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of MLEs, AIC and BIC of Exponential, Rayleigh, Weibull, BS, LBS and Laplace BS distributions for Cavía Porcellus data. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & **Q1** & **Q2** & **Q3** & **Mean** & **Kurtosis** & **Skewness** & **SD** \\ \hline Sample & 130 & 160 & 292 & 280.1667 & 8.0993 & 2.3223 & 303.1249 \\ \hline Exponential & 80.5989 & 194.1967 & 388.3935 & 280.1667 & 9 & 2 & 280.1667 \\ \hline Rayleigh & 4311.0799 & 482.8679 & 682.8783 & 363.4507 & 3.2451 & 0.6311 & 268.6781 \\ \hline Weibull & 92.9533 & 208.0012 & 392.4504 & 281.4662 & 7.4714 & 1.7535 & 258.0723 \\ \hline BS & 75.1050 & 162.4521 & 351.3837 & 274.0991 & 14.7086 & 2.7626 & 314.0061 \\ \hline LBS & 96.6347 & 179.6688 & 334.0506 & 276.9076 & 23.1251 & 11.8393 & 323.9002 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: EDA outcomes based on Head and Neck Cancer data.