## 3 Results
The tails of the normal distribution were too thin to produce enough extreme events to match those in the sample. In other words, the likelihood that NiTi alloys would produce a large value of corrosion rate was high. Therefore, distribution families must be considered that might represent these prominent parts better. It is more convenient to consider the corrosion rate as a random variable, bearing in mind that corrosion processes are influenced by a large number of factors of stochastic nature, especially in the seawater environment [47]. A probabilistic method of fitting three-parameter continuous probability functions is proposed here, to describe the stochastic nature of the monthly corrosion rate of the observed NiTi-1 and NiTi-2 alloys in three different seawater environments. The Probability Density Function (PDF) of a continuous function, denoted as \(f(x)\), is the probability that the variate has the value \(x\). The Cumulative Distribution Function (CDF), denoted as \(F(x)\), is the probability that the variate X takes a value less than, or equal to, a value \(x\). There is a relation between PDF and CDF of a continuous distribution: \(F(x)=P(X\leq x)=\int_{-\infty}^{x}f(s)ds\), or when PDF exists \(f(x)=F(x)^{\prime}=\frac{dF(x)}{dx}\). The empirical CDF of the sample is defined at a point \(x\) as the proportion of elements in the sample that are less than, or equal to, \(x\). Assuming that the \(x\)-axis is divided into intervals of equal width, the empirical PDF is defined as the quotient of the relative frequencies of the sample indices located in the observed interval and the width of the interval. For example, empirical CDFs of corrosion rate \(c_{1}\) of the NiTi-1 and NiTi-2 alloys (denoted as \(F_{1}(c_{1})\) and \(F_{2}(c_{1})\), respectively) are shown in Figure 10. Empirical PDF for the NiTi-1 alloy can be seen in Figures 11 and 12 in histogram form. Additionally, empirical CDF of corrosion rate \(c_{1}\) of the NiTi-1 alloy is presented as a step function in Figure 13.  
Three-parameter probability distribution functions are characterised by three parameters: Location, scale and shape parameter. The location parameter \(p\) shifts the PDF function \(f(x)\) along the \(x\)-axis by the value of \(p\), i.e., \(f(x-p)\). The scale parameter determines the width of the PDF function \(f(x)\). More precisely, for larger-scale parameter values, the PDF function is wider. A shape parameter is any parameter that cannot describe the location and/or width of a PDF function, and cannot be represented as a function of these two  
Figure 10: Empirical CDF of the NiTi-1 and NiTi-2 alloys. parameters. Not all theoretical distributions depend on three parameters, so there are one-parameter, two-parameter and multiparameter distributions. However, in this paper, the research is focused only on the analysis of three-parameter distributions. A total of 27 different three-parameter continuous PDF functions are considered, in order to describe the stochastic nature of the corrosion rate denoted as \(c_{1}\) best. Figure 11: Empirical PDF and the three best fitted three-parameter distributions of the NiTi-1 alloy corrosion rate in the air environment. Figure 12: Empirical PDF and the three best fitted three-parameter distributions of NiTi-1 alloy corrosion rate in a tide environment. One of the main problems that arise when fitting theoretical distributions into empirical data is the ubiquity of oscillations in the measured values and the large variability of the data. Large changes in distribution tails produce large residuals and reduce the goodness of fit, with the result that testing statistical hypotheses becomes a highly non-trivial problem. The presented corrosion rate empirical data have a complex structure, resulting in difficulties in understanding which theoretical continuous distribution would best follow changes in empirical data.