## 3 Results
### Results of Statistical Analysis for the NiTi-1 alloy
\begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{4}{c}{**Air**} \\ \hline
**Lower Bound** & **Upper Bound** & **Empirical PDF of \(\mathbf{c_{1}}\)** & \(f_{\mathbf{a_{1}}}^{(\mathrm{I})}\) & \(f_{\mathbf{a_{1}}}^{(\mathrm{f})}\) & \(f_{\mathbf{a_{1}}}^{(\mathrm{b})}\) \\ \hline
2 & 2.5045 & 0.148 & 0.18829 & 0.17834 & 0.15185 \\ \hline
2.5045 & 3.009 & 0.333 & 0.27567 & 0.28288 & 0.30930 \\ \hline
3.009 & 3.5135 & 0.241 & 0.18676 & 0.18733 & 0.18950 \\ \hline
3.5135 & 4.018 & 0.019 & 0.11154 & 0.11138 & 0.10980 \\ \hline
4.018 & 4.5225 & 0.000 & 0.06776 & 0.06814 & 0.06780 \\ \hline
4.5225 & 5.027 & 0.037 & 0.04315 & 0.04376 & 0.04420 \\ \hline
5.027 & 5.5315 & 0.000 & 0.02882 & 0.02944 & 0.03009 \\ \hline
5.5315 & 6.036 & 0.074 & 0.02009 & 0.02061 & 0.02122 \\ \hline
6.036 & 6.5405 & 0.093 & 0.01451 & 0.01492 & 0.01541 \\ \hline
6.5405 & 7.045 & 0.056 & 0.01080 & 0.01112 & 0.01147 \\ \hline \multicolumn{5}{c}{**Tide**} \\ \hline
**Lower Bound** & **Upper Bound** & **Empirical PDF of \(\mathbf{c_{1}}\)** & \(f_{\mathbf{f_{1}}}^{(\mathrm{b})}\) & \(f_{\mathbf{f_{1}}}^{(\mathrm{f})}\) & \(f_{\mathbf{f_{1}}}^{(\mathrm{d})}\) \\ \hline
1 & 1.743333 & 0.017 & 0.00959 & 0.00808 & 0.00776 \\ \hline
1.743333 & 2.486667 & 0.133 & 0.19950 & 0.21955 & 0.21636 \\ \hline
2.486667 & 3.23 & 0.433 & 0.35833 & 0.32213 & 0.31896 \\ \hline
3.23 & 3.973333 & 0.167 & 0.19035 & 0.20092 & 0.19905 \\ \hline
3.973333 & 4.716667 & 0.033 & 0.09372 & 0.10316 & 0.10625 \\ \hline
4.716667 & 5.46 & 0.050 & 0.05078 & 0.05412 & 0.05750 \\ \hline
5.46 & 6.203333 & 0.033 & 0.02989 & 0.03037 & 0.03269 \\ \hline
6.203333 & 6.946667 & 0.117 & 0.01876 & 0.01822 & 0.01958 \\ \hline
6.946667 & 7.69 & 0.000 & 0.01238 & 0.01158 & 0.01229 \\ \hline
7.69 & 8.433333 & 0.017 & 0.00851 & 0.00772 & 0.00804 \\ \hline \multicolumn{5}{c}{**Sea**} \\ \hline
**Lower Bound** & **Upper Bound** & **Empirical PDF of \(\mathbf{c_{1}}\)** & \(f_{\mathbf{s_{1}}}^{(\mathrm{g})}\) & \(f_{\mathbf{s_{1}}}^{(\mathrm{d})}\) & \(f_{\mathbf{s_{1}}}^{(\mathrm{gp})}\) \\ \hline
0 & 4.75275 & 0.000 & 0.02808 & 0.02958 & 0.02285 \\ \hline
4.75275 & 9.5055 & 0.179 & 0.07661 & 0.08017 & 0.10774 \\ \hline
9.5055 & 14.25825 & 0.075 & 0.13488 & 0.12560 & 0.16092 \\ \hline
14.25825 & 19.011 & 0.119 & 0.17146 & 0.16283 & 0.14874 \\ \hline
19.011 & 23.76375 & 0.164 & 0.17137 & 0.17866 & 0.13570 \\ \hline
23.76375 & 28.5165 & 0.224 & 0.14352 & 0.15896 & 0.12160 \\ \hline
28.5165 & 33.26925 & 0.090 & 0.10540 & 0.11273 & 0.10607 \\ \hline
33.26925 & 38.022 & 0.045 & 0.07004 & 0.06728 & 0.08852 \\ \hline
38.022 & 42.77475 & 0.015 & 0.04293 & 0.03689 & 0.06758 \\ \hline
42.77475 & 47.5275 & 0.090 & 0.02455 & 0.01989 & 0.03880 \\ \hline \end{tabular}
\end{table} 
Table 9: The empirical values and the values of PDF for the three best-fitted distributions for \(c_{1}\) concerning NiTi-1. Figures 11-13 show the PDF and CDF graphs of the three best-fitted distributions for the air, tide and sea environments in the case of the NiTi-1 alloy, respectively. These graphs also contain a representation of the empirical PDF or the empirical CDF accordingly. These figures correspond to the numerical results given in Tables 9 and 10.