## 4 Results and Analysis
### Data Preparation
In category D, 85% employees are availing healthcare services. Table 9 depicts the package for category E, all employees whose ages are less than and equal to 28, male and married are in group I and all employees whose ages are greater than and equal to 29, female and married are in group II. The premium amount for each employee in group I is 54,665 rupees and the premium amount for each employee in group II is 13,802. The original number of employees in category E is 1991. In category E, 50% of employees are availing health care services. In Table 10 package for the category, F is shown, all employees whose ages are 28, and are male and married are in one group and all employees whose ages are 26, and are female and single are in group II. In this category, only 40% are using healthcare services. The premium amount for each employee in group I is 41,191 and for each employee in group II is 7,768. Table 11 depicts the package for category G. Employees who are married, male and aged less than and equal to 30 are in group I and all-female employees with age greater than and equal to 30, married are in group II. The premium amount for each employee in group I is 96,912 rupees and the premium amount for each employee in group II is 19,656. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Age** & **Gender** & **Relation Status** & **Sum Amount** & **Amount** & **Visit** \\ \hline
28.0 & 1.0 & 1.0 & 2,460,744 & 17,208.0 & 3003.0 \\
29.0 & 0.0 & 1.0 & 18,693,312 & 58,784.0 & 21,306.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Need based Package for Category C. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Age** & **Gender** & **Relation Status** & **Sum Amount** & **Amount** & **Visit** \\ \hline
28.0 & 0.0 & 1.0 & 2,488,048 & 54,088.0 & 3036.0 \\
29.0 & 0.0 & 0.0 & 1,697,484 & 10,812.0 & 1727.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Need based Package for Category D. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Age** & **Gender** & **Relation Status** & **Sum Amount** & **Amount** & **Visit** \\ \hline
28.0 & 0.0 & 1.0 & 30,557,735 & 54,665.0 & 36,894.0 \\
29.0 & 1.0 & 1.0 & 4,182,006 & 13,802.0 & 5151.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Need based Package for Category E.  
Similarly, gamma parameters for all categories E, F and G are computed as shown in Table 15.  
Table 16 depicts the number of out of pocket employees in the current medical benefits amount and out of pocket employees in optimized benefit amount using Gamma distribution. The term out of pocket is used to explain how many employees are spending additional amounts for availing healthcare services and getting financially overburdened. In Figure 14, outlier are detected and these outliers are basically depicting the out of pocket employees in each category. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline \multirow{2}{*}{**Category**} & **Out of Pocket Employees in Current Amount** & **Out of Pocket Employees in Optimized Amount** \\ \hline A & 45 & 33 \\ \hline B & 30 & 10 \\ \hline C & 54 & 33 \\ \hline D & 47 & 15 \\ \hline E & 57 & 31 \\ \hline F & 52 & 12 \\ \hline G & 30 & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 16: Out of Pocket Employees in Current Medical Benefit and in Optimized Amount. Figure 13: HISTFIT for group 2 in Category D.  
In Figure 15, out of pocket employees before and after medical benefit optimization are shown. The y-axis on the left side is depicting the number of out-of-pocket employees and the y-axis on the right side is depicting the number of out of pocket employees after optimization. The x-axis is depicting categories used for insurance coverage. In Table 17, the gamma distribution is depicted for each group in all categories. If we move to the right of gamma distribution each time by adding \(\mu\) to \(\sigma\).