## 3 Results
### Results of Statistical Analysis for the NiTi-1 alloy
However, the Standard Deviations for the Frechet and Burr distributions can be calculated, and they are equal to 5.1893 nm/month and 2.4959 nm/month, respectively. Generally speaking, if the procedure of fitting theoretical distributions is carried out correctly, the mean values of the fitted distributions always take values that are close to the mean value of the parameter \(c_{1}\). Influenced by the tide, the Burr, shifted Log-Logistic, and Dagum distributions have proven to be the three best-fitted tree parameter distributions to describe monthly corrosion rate behaviour. The terms describing their PDF (\(f_{t_{1}}^{(b)}(x)\), \(f_{t_{1}}^{(l)}(x)\), \(f_{t_{1}}^{(d)}(x)\)) and CDF (\(F_{t_{1}}^{(b)}(x)\), \(F_{t_{1}}^{(l)}(x)\), \(F_{t_{1}}^{(d)}(x)\)) are given in Equations (17)-(22), respectively. \[f_{t_{1}}^{(b)}(x)=\frac{0.354244}{\left(1+0.52122x^{0.28059}\right)^{3.4222}x ^{0.71941}},\ x>0, \tag{17}\]  
\[f_{t_{1}}^{(l)}(x)=\frac{0.7836231442446434(x-1.5086)^{1.5145}}{\left(1+0.3116 417356311964(x-1.5086)^{2.5145}\right)^{2}},\ x\geq 1.5086, \tag{18}\]  
\[f_{t_{1}}^{(d)}(x)=\frac{0.09246162125573458x^{99.405731}}{\left(1+0.784561458 9000012x^{3.4851}\right)^{29.81}},\ x\geq 0. \tag{19}\]  
\[F_{t_{1}}^{(b)}(x)=1-\frac{1}{\left(1+0.52122x^{0.28059}\right)^{2.4222}},\ x>0 \tag{20}\]  
\[F_{t_{1}}^{(l)}(x)=\frac{1}{1+3.20881\Big{(}\frac{1}{x-1.5086}\Big{)}^{2.5145}}, \ x\geq 1.5086, \tag{21}\]  
\[f_{a_{1}}^{(b)}(x)=\frac{0.238961}{\left(1+0.638258x^{0.15485}\right)^{3.4178}x^{0. 84515}},\ x\geq 0. \tag{13}\]0  
In the case of the influence of the tide on the corrosion rate of the NiTi-1 alloy, for the previously defined Burr, shifted Log-Logistic, and Dagum distributions, mean values equal to 3.6334 nm/month, 3.6023 nm/month and 3.5806 nm/month, respectively, were determined, while the Standard Deviations were 2.419 nm/month, 2.4808 nm/month and 1.8852 nm/month, respectively. It is noticeable that all mean values were very close to the mean value for the corrosion rate obtained in Equation (3). Taking into account the probability estimates given by Equation (10) and the PDF of the best fitted Burr distribution in the case of tide influence, it was possible to calculate probabilities for corrosion wear as follows:  
\[f_{a_{1}}^{(b)}(x)=\frac{0.238961}{\left(1+0.638258x^{0.15485}\right)^{3.4178}x^{0. 84515}},\ x\geq 0. \tag{13}\]1  
where \(t>0\) (months) is the elapsed time of the tide's influence on the NiTi-1 alloy, and \(0<c_{a}<c_{b}\). If values \(c_{a}=0\), \(c_{b}=4\) nm/month, and \(t=6,\ 12,\ 18\) months are replaced into Equation (17), the following estimates can be calculated for probabilities:  
\[ \begin{array}{ll}P(d(6)\leq 24\ \text{nm})&=P(d(12)\leq 48\ \text{nm})=P(d(18) \leq 72\ \text{nm})\\ &=\int\limits_{0}^{4}\frac{0.354244}{(1+0.52122x^{0.28069})^{3.4222}x^{0.71941 }}dx=0.76236.\end{array}  \tag{24}\]  
The generalised extreme value (GEV), Dagum and Generalized Pareto distributions describe the changes in the monthly corrosion rate caused by the sea best in the case of the NiTi-1 alloy. The corresponding PDF (\(f_{s_{1}}^{(g)}(x)\), \(f_{s_{1}}^{(d)}(x)\), \(f_{s_{1}}^{(gp)}(x)\)) and CDF (\(F_{s_{1}}^{(g)}(x)\), \(F_{s_{1}}^{(d)}(x)\), \(F_{s_{1}}^{(gp)}(x)\)) expressions are shown in Equations (25)-(30), respectively.