## 3 Statistical and Correlation Analysis  
The type and character of the statistical distribution, in addition to the homogeneity of the general samples, can indicate the physical mechanisms responsible for the appearance of one or another kind of disturbance [17]. For example, a normal distribution is formed from the summing up effect of many random, weak independent impacts. In a closed system, the energy of its components is distributed according to the exponential law or the Laplace law. A random multiplicative set of several parameters leads to a log-normal distribution, etc.  
The results of the statistical analysis of the GIC values from VKH station \(\,\mathrm{|f|}\,\) and the geomagnetic field variability \(\,\mathrm{|dY/dt|}\,\) are shown in Figures 3a and 3b respectively. The calculated probability density function (PDF), the survival function (SF), and the empirical survival function (ESF) reveal that the distribution of both parameters is best described by the log-normal distribution. Starting from a -99.3 percentile, a heavy tail can be traced, corresponding to generalized Pareto distribution law.  
Figure 2: A fragment of the time series (averaged over 15-min intervals) of the initial data, comprising the magnetic storm on 17 March 2015. In the time series of the Y component of the geomagnetic variations, the baseline has been excluded.  
Analysis of the intensity of the geomagnetic variations of the Y-component from neighboring to VKH magnetic stations KEV, SOD, and LOZ (Table 1) found a distribution of variability values \(\mid\!dY/dt\!\mid\) similar to that shown in Figure 3. It indicates that fluctuations of both GIC amplitude and local geomagnetic field variability are determined mainly by rare intense deviations, probably due to substorm activity and geomagnetic pulsations in the Pc5-Pi3 range [18]. At the same time, there are a number of research studies that have found that it is convective periods that generate the extremes, rather than pulsations [19]. This situation may indicate the need for additional research in this area.  
The analysis of the distribution of the regional IE-index characterizing the magnetic disturbance in the auroral zone [20] demonstrates the structural similarity of the statistics. However, the distribution (not shown) predominantly corresponds to the exponential law with exponential tails.  
Table 3 represents the results of assessing the Pearson correlation coefficient \(r\) between the GIC values and the corresponding geomagnetic data. In order to reduce the influence of the stochastic component on the result, at this stage, the time series are averaged over 15-min intervals, taking into account that the duration of a substorm and the time interval between two following substorms are both usually at least 30 min.  
The values of the Pearson correlation coefficient (Table 3) correspond to the ranking of the statistical test for the compliance of heavy tails to the generalized Pareto law results. It eliminates the cases of the false correlation and is well explained by the spatial (km) and latitudinal (\({}^{\circ}\) N) separation of magnetic stations from the VKH station (Table 1). The statistics obtained indicates the consistency of the results with physical laws and geostatistical principles.