## 4 Results of Experimental Studies
### Approximation of Experimental Data by Theoretical Distributions  
The procedure for approximating experimental FFS distributions of cars consists of replacing empirical frequencies with theoretical ones determined by mathematical dependencies of the theoretical distribution. The choice of the type of theoretical distribution model is made either on the basis of a meaningful analysis of the previously obtained statistical characteristics of the studied quantity or based on general considerations based on a visual analysis of the obtained distribution graphs. As already mentioned, most authors use relatively simple one- or two-parameter distributions to describe the FFS distribution. In order to approximate the experimental FFS distributions of cars on the road network of the city of Kharkiv, it was decided to check four standardized laws of distribution: Normal, Log-normal, Gamma, and Chi-square. Dependencies of the functions of these distribution laws can be taken from any reference book on mathematical statistics. For example, the normal distribution function in our case will look like the following:  
\[f(v)=\frac{1}{\sigma\cdot\sqrt{2\pi}}\cdot e^{-\frac{(v-m)^{2}}{2\sigma^{2}}} \tag{4}\]  
where \(v\) is the value of speed; \(m\) is the average speed value; and \(\sigma\) is the root mean square deviation. Thus, the parameters of the normal distribution are \(m\) and \(\sigma\). The Gamma distribution function is expressed as follows:  
\[f(v)=\frac{1}{\Gamma(\lambda)}\cdot V^{\lambda-1}\cdot e^{-\beta\cdot v} \tag{5}\]  
where \(\Gamma(\lambda)\) is the Gamma function; \(\lambda\) is the shape parameter; and \(\beta\) is the scale parameter. The function of the Log-normal distribution is expressed as follows:  
\[f(v)=\frac{1}{v\cdot s\cdot\sqrt{2\pi}}\cdot e^{-\frac{1}{2}\cdot\left(\frac{ \ln(v)-\pi}{s}\right)^{2}} \tag{6}\]  
where \(\mu\) is the average arithmetic logarithm of the speed and \(s\) is the standard deviation of the logarithm of the speed. Figure 3: Polygonal and cumulative plots of the distribution of FFS values. The function of the Chi-squared distribution is expressed as follows:  
\[f(v)=\frac{\left(\frac{1}{2}\right)^{\frac{k}{2}}}{\Gamma\left(\frac{k}{2}\right) }\cdot v^{\frac{k}{2}-1}\cdot e^{-\frac{k}{2}} \tag{7}\]  
where \(k\) is the number of degrees of freedom. The degree of reliability of the approximation of the experimental FFS distribution by the theoretical distribution law can be established using standard consistency criteria. In this study, the Pearson test was used, the characteristics of which are the discrepancy parameter \(\chi^{2}\), the number of degrees of freedom \(d_{f}\), and the calculated value of the \(p\)-value \(p\). At the same time, the limit on the value of the theoretical frequencies when calculating the Pearson criterion was set at the level of \(f(i)\geq 5\). FFS distribution histograms with superimposed graphs of theoretical distribution laws for the section of Ave. The heroes of Kharkiv (Stat. 1) are shown in Figure 4. The values of the relevant parameters of the distribution laws and consistency criteria are given in Table 5.  
Conclusions about the validity of the hypothesis about the law of distribution can be made by focusing on the empirical value of the criterion \(\chi^{2}\) or on the calculated value of the \(p\)-value \(p\), which can be compared with the accepted significance level, which in our case can be accepted at the level of \(\alpha=0.05\). It can be seen in Table 5 that the condition \(p>\alpha\) is fulfilled for all distributions, so the hypothesis that the theoretical distributions correspond to the experimental data can be accepted. Thus, for the section of the main street Ave. Heroes of Kharkiv, FFS distribution can be described with sufficient practical accuracy by any of the four proposed distribution laws. Greater accuracy is provided by  
Figure 4: Approximation of FFS experimental data by theoretical distribution laws for the section Ave. Heroiv Kharkova.