## 3 Results
### Results of Statistical Analysis for the NiTi-2 Alloy
Taking into account Equation (51), the independence of the variables X and Y, and the definition for CDF, the corresponding CDF for the random variable Z can be obtained as follows:  
\[F_{Z}(z)=P(X-Y\leq z)= \int_{-\infty}^{z}f_{Z}(t)dt=\int_{-\infty}^{z+y}f_{X}(x)dx\int_{- \infty}^{\infty}f_{Y}(y)dy=\int_{-\infty}^{\infty}F_{X}(z+y)f_{Y}(y)dy, \tag{52}\]  
For each of the three considered seawater environments it is necessary to replace in Equation (52) the adequate expressions for CDF and PDF of the best-fitted distributions  
Figure 18: Comparative view of the NiTi-1 and NiTi-2 empirical CDFs in three seawater environments. shown in Section 2. For example, if the corrosion rate difference for air is observed, the CDF from Equation (14) and a PDF from Equation (31) have to be incorporated in Equation (52). In the case of the selected best three-parameter distributions, the combination of the corresponding CDF and PDF functions results in complex integrated functions that are very complicated to integrate, primarily because the exponents and coefficients are decimal values. For the evaluation of such convolutional integrals, it is convenient to apply numerical integration, i.e., numerical convolution. In the background of this algorithm is a very complex recursive procedure involving Cubic spline interpolation and the Five-point Lobotto quadrature formula. A concise description of the numerical convolution algorithm can be found in [67], while a detailed overview of this method is given in [68]. Figure 19 presents the PDF of the NiTi-1 and NiTi-2 alloys corrosion rate differences caused by distinct seawater environment influences. The values of the presented probabilities of the differences between the corrosion rate alloys of NiTi-1 and NiTi-2 were obtained by numerical integration of the corresponding convolutions, formed based on the PDF functions of the best-fitted three-parameter distributions, presented in Section 2. The PDF graph of the NiTi-1 and NiTi-2 alloys corrosion rate differences under air influence, shown at the far left in Figure 19 is very narrow, with a noticeable peak. Based on this, it was concluded that under the influence of air, the probability of a difference in the corrosion rate of these two NiTi alloys was very high in cases where the difference was manifested. The graph is shifted slightly in the negative direction of the \(x\)-axis. This fact indicates that, under the influence of air, NiTi-1 alloys generally develop a lower degree of corrosion. The values of the measured differences in the corrosion rate occurred mainly within the interval \([-5\text{nm},5\text{nm}]\). The PDF function reached its maximum for corrosion rate difference \(z=c_{a}^{(1)}-c_{a}^{(2)}=-0.37\) nm and the corresponding probability was 0.368778. In the conditions of the influence of the tide on the corrosion processes, the observed NiTi alloys show the most significant differences, as shown in the PDF graph of the corrosion rate (middle graph in Figure 19). This graph was shifted significantly to the left and tilted slightly to the right. Almost all values of corrosion rate differences are located on the negative side of the \(x\)-axis, which means that the NiTi-1 alloy in tidal conditions shows favourable characteristics with respect to the NiTi-2 alloy. Namely, the values of the corrosion rate of the NiTi-1 alloy were almost always lower than the corrosion rate values for the NiTi-2 alloy. However, the associated probabilities were less than the probability of the corrosion rate differences caused by air. The highest probability value was 0.0831721, and it was obtained for the corrosion rate difference \(z=c_{t}^{(1)}-c_{t}^{(2)}=-4.005\) nm. The PDF for corrosion rate difference is shown in the far-right graph in Figure 19. This graph is almost symmetrical with the \(y\)-axis as the axis of symmetry, which is not surprising considering that statistical analysis showed that the NiTi-1 and NiTi-2 alloys  
Figure 19: PDF of the NiTi-1 and NiTi-2 alloys corrosion rate differences under air, tide and sea influences.