## 3 Results
### Results of Statistical Analysis for the NiTi-1 alloy  
In the process of statistical analysis of the NiTi-1 alloy, 27 different continuous theoretical distributions were fitted in empirical data for each of the three observed seawater environments. The obtained distributions were then ranked based on the values of the KS statistics. The three best-fitting three-parameter distributions were obtained in this way [55]. To verify the validity of the obtained functions, the resulting distributions were additionally ranked based on the values of the AD statistics. Table 7 shows the three best-fitted three-parameter distributions for corrosion rates in the case of the NiTi-1 alloy, in air, tide and sea environments, as well as the corresponding rankings based on the KS and AD tests. Fitted distributions are shown with the most adequate values of location, scale, and shape parameters, which were obtained by the maximum likelihood estimation method. Taking into account the calculated best values of the three parameters, as well as the standard analytical expressions describing the PDF and CDF of the considered distributions, the formulas for PDF and CDF of the best-fitted theoretical distributions from Table 7 are given below. The three fitted distributions (in the case of the NiTi-1 alloy) that describe the monthly corrosion rate that occurred under the influence of air best are the shifted Log-logistic, Frechet and Burr distributions, respectively. The expressions representing the corresponding PDFs of these distributions (\(f_{a_{1}}^{(l)}(x)\), \(f_{a_{1}}^{(f)}(x)\), \(f_{a_{1}}^{(b)}(x)\)) are given in Equations (11)-(13), while the expressions for the CDF (\(F_{a_{1}}^{(l)}(x)\), \(F_{a_{1}}^{(f)}(x)\), \(F_{a_{1}}^{(b)}(x)\)) of these distributions are shown in Equations (14)-(16). \[f_{a_{1}}^{(l)}(x)=\frac{1+62206(x-2.0076)^{0.879}}{\left(1+0.863256(x-2.0076)^ {1.879}\right)^{2}},\ x\geq 2.0076, \tag{11}\]  
\[f_{a_{1}}^{(f)}(x)=\frac{1.06996e^{-\frac{1.25658}{(x-1.8696)^{0.88151}}}}{(x- 1.8696)^{1.85151}},\ x>1.8696, \tag{12}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Environment** & **Distribution (Parameters)** & **KS Ranking** & **AD Ranking** \\ \hline \multirow{4}{*}{Air} & Log-Logistic (1.879, 1.0814, 2.0076) & 1 & 3 \\ \cline{2-4}  & Fréchet (0.85151, 1.3076, 1.8696) & 2 & 2 \\ \cline{2-4}  & Burr (0.15485, 18.168, 2.4178) & 3 & 1 \\ \hline \multirow{4}{*}{Tide} & Burr (0.28059, 10.198, 2.4222) & 1 & 1 \\ \cline{2-4}  & Log-Logistic (2.5145, 1.5899, 1.5086) & 2 & 2 \\ \cline{2-4}  & Dagum (28.81, 3.4851, 1.0721) & 3 & 3 \\ \hline \multirow{4}{*}{Sea} & GEV (\(-\)0.11404, 9.9232, 17.683) & 1 & 2 \\ \cline{2-4}  & Dagum (0.33963, 5.5711, 30.551) & 2 & 1 \\ \cline{1-1} \cline{2-4}  & General Pareto (\(-\)0.64068, 27.101, 5.878) & 3 & 12 \\ \hline \end{tabular}
\end{table} 
Table 7: The three best-fitted three-parameter distributions for the NiTi-1 alloy in air, tide and sea environments. \[f_{a_{1}}^{(b)}(x)=\frac{0.238961}{\left(1+0.638258x^{0.15485}\right)^{3.4178}x^{0. 84515}},\ x\geq 0. \tag{13}\]  
\[F_{a_{1}}^{(l)}(x)=\frac{1}{1+1.1584\Big{(}\frac{1}{x-2.0076}\Big{)}^{1.879}},\ x\geq 2.0076, \tag{14}\]  
\[F_{a_{1}}^{(f)}(x)=e^{-\frac{1.2455}{(x-1.8696)^{0.88515}}},\ x>1.8696, \tag{15}\]  
\[F_{a_{1}}^{(b)}(x)=1-\frac{1}{\left(1+0.638258x^{0.15485}\right)^{2.4178}},\ x>0. \tag{16}\]  
Mean values can be calculated for the previously determined Log-logistic, Frechet and Burr distributions, and they are equal to 3.8249 nm/month, 3.7878 nm/month and 3.7208 nm/month, respectively. It is noticeable that these values are very close to the mean value for the corrosion rate determination in Equation (2). As this Log-Logistic distribution is a shifted standard Log-Logistic distribution, its variance, as well as the Standard Deviation cannot be calculated based on the set of these particular parameters, because, according to the formula for variance, the obtained value takes a negative value.