## 3 Results  
Based on the observations \(\mu_{x,t}\) and the procedure described in Section 2.4, the variability of dispersion throughout the intervals seemed to occur mainly among women and men between 30 and 40 years of age (with some exceptions for both women and men). Apart from a woman/man 30-40 years old, the Fisher F-test for variance did not show significant differences in terms of lower and higher dispersion periods based on the F statistic. The obtained results are divided into two subgroups: one of them with significant differences between lower and higher dispersion and the second one in another case. The first group includes, for example, a 37-year-old woman \((F_{37})\), a 32-year-old man \((M_{32})\), a 36-year-old man \((M_{36})\), and a 37-year- old man \((M_{37})\). The second group, for example, consists of a 35-year-old woman \((F_{35})\) and a 22-year-old man \((M_{22})\). The above results are presented in Tables 1 and 2 and Figures 1-7 (source of empirical data: [38; 39]). Figure 2: The values of mortality rates—female, age 37: empirical (Emp), theoretical (LC, nGMs), forecasts (nGMsf), and c. interval based on the LC, and nGM model with Markov switch. Figure 4: The values of mortality rates—male, age 36: empirical (Emp), theoretical (LC, nGs), forecasts (nGsf), and c. interval based on the LC, and nGs model with switch. Figure 3: The values of mortality rates—male, age 32: empirical (Emp), theoretical (LC, nGMs), forecasts (nGMsf), and c. interval based on the LC, and nGM model with Markov switch. Figure 5: The values of mortality rates—male, age 37: empirical (Emp), theoretical (LC, nGs), forecasts (nGsf), and c. interval based on the LC, and nGs model with switch. Figure 6: The values of mortality rates—female, age 35: empirical (Emp), theoretical (LC, nGs), forecasts (nGsf), and c. interval based on the LC, and nGs model with switch. Figure 1 shows an example of an empirical \(\mu_{x,t}\) from 1958-2019, regarding periods with lower and higher dispersion in the case of \(F_{37},M_{32},M_{36}\), and \(M_{37}\). Additionally, the example points to a lack of statistical differences between periods in cases \(F_{35}\) and \(M_{22}\). In Figures 2-7, the observed (blue circular points) and theoretical values of the \(\mu_{x,t}\) (using the Formulas (61) and (62)) mortality rates based on the Lee-Carter (red squares), nGs or nGMs (green diamonds) models from 1958-2019 (HMD) are presented. Moreover, the forecast (purple diamonds) and the yellow and sienna lines define 95% (Cl95) and 90% (Cl90) confidence intervals. In the case of \(F_{37},M_{32}\), and \(M_{36}\), the data were split into three periods of lower, higher, and again lower dispersion. In the case of \(M_{37}\), it is possible to distinguish an initial period with a higher dispersion (in the years 1958-1963), but the number of observations is not sufficient to estimate all parameters of the model (61)-(62) \begin{table}
\begin{tabular}{c c c c c c} \hline
**Age** & \(MSE_{EM\_LC}\) & \(MSE_{EM\_nG}\) & \(MSE_{EM\_nG}\) & \(F_{1}(pv)\) & \(F_{2}(pv)\) \\ \hline \(F_{37}\) & \(5.265\times 10^{-9}\) & \(1.720\times 10^{-8}\) & \(4.849\times 10^{-9}\) & 0.195 (0.02) & 8.69 (0.004) \\ \(M_{32}\) & \(2.122\times 10^{-8}\) & \(7.639\times 10^{-8}\) & \(1.762\times 10^{-8}\) & 0.22 (0.03) & 0.18 (0.02) \\ \(M_{36}\) & \(9.591\times 10^{-8}\) & \(1.873\times 10^{-7}\) & \(3.701\times 10^{-8}\) & 0.12 (0.01) & 5.15 (0.02) \\ \hline \(M_{37}\) & \(4.818\times 10^{-8}\) & \(2.481\times 10^{-8}\) & – & 0.27 (0.0197) & \(\begin{array}{c}192\\ (2.7\times 10^{-23})\end{array}\) \\ \hline \(F_{35}\) & \(3.74\times 10^{-9}\) & \(2.471\times 10^{-9}\) & – & – & – \\ \(M_{22}\) & \(1.728\times 10^{-8}\) & \(1.319\times 10^{-8}\) & – & – & – \\ \hline \end{tabular}
\end{table} 
Table 1: MSE (goodness of fit), F-statistics, \(p\)-value (\(pv\)).