## 5 Statistical Analysis of Quality of IoT Service during the Year
Equation (1) is a mathematical formulation of the aforementioned PDF, while the comparison of modeled PDF and empirical data is shown in Figure 19.  
Please note that:  
\[1+k\frac{(x-\mu)}{\sigma}>0 \tag{2}\]  
Parameters needed to achieve a desired PDF are:  
* \(k=-0.095368\),
* \(\sigma=2.8064\),
* \(\mu=13.3195\). As it can be seen from Figure 19 there are some differences between the empirical data and modeled PDF, which are presented with red and orange lines, respectively. These differences cause that difference in CDFs of empirical and modeled data (blue line, denoted with Empiric/Modeled (E/M) Difference) goes over the boundaries set by the Kolmogorov-Smirnoff (K-S) test (purple and green lines, denoted with the Upper K-S Boundary and Lower K-S Boundary). However, although some irregularities exist, it may still be said that the modeled PDF can be used to describe behavior of the empirical data with a good accuracy, because K-S boundary is violated for only \(\sim\)5% of samples with the maximum violation of \(\sim\)6%. Next, the worst matching case (July 2018) is presented. Matlab software package is once again used for the analysis and it is concluded that generalized extreme value PDF again gives the best results. Naturally, the parameters are different and they are:  
* \(k=-0.13687\),  
Figure 19: Statistical modeling for June 2018. From Figure 20 it can be seen that the differences between the modeled and empirical data are greater than in the previous case. This is easily observed either by comparing PDFs or the differences between CDFs, which consequently goes over the Kolmogorov-Smirnoff test boundaries on multiple occasions. However, of all the tested PDFs the one presented here gives the best results (K-S boundary is violated for \(\sim\)15% of samples with the maximum violation of \(\sim\)20%) and it is taken as a mathematical model of the empirical data. Based on the presented analysis it may be said that modeled PDFs can be reliably used to describe and predict the IoT OTH maritime surveillance service behavior. This can be further used in order to increase the data fusion process stability and thus reliability of the IoT OTH maritime surveillance service as a whole. During the harsh weather conditions, the satellite link can perform poorly, and numerous packet retransmissions might occur and TCP connection might be disrupted. In case when the detection file is not transmitted timely to the central location this can lead to dropping the detection file at the radar location. This is due to the detection file no longer being relevant and thus not being eligible for use in the data fusion process at the C2 center. For that reason, we have observed the outage probability using the following definition: Po = Nt/Ntot, where Po is the outage probability, Nt is the number of unsuccessfully (not on time) delivered detection files to C2 center, and Ntot is the total number of generated detection files at the radar location. In Figure 21 the outage probabilities are shown for the three rainiest and the three driest months as we expect that the rainier months should have a greater outage probability. Figure 21 shows that the rainier months indeed have a greater outage probability which comes from worse weather conditions on average (Po: 0.1-0.25% in good weather conditions, 0.35-0.7% in bad weather conditions). Figure 20: Statistical modeling for July 2018. In this section, we have derived the IoT OTH maritime surveillance service performance dependency on weather conditions, as a function of data latency.