This letter analyzes the vertical coordinates of 2713 global navigation satellite system (GNSS) stations in Europe, each with data spanning over three years, to assess whether they follow a normal distribution based on skewness and kurtosis values. Subsequently, a power-law noise analysis was conducted to compute spectral indices for all stations, as well as for those that meet the normality criterion. The spatial distribution of skewness, kurtosis, and spectral indices was visualized on maps using inverse distance weighting (IDW) interpolation. The study demonstrated that the spectral index maps remain largely unchanged regardless of whether the data meet the normal distribution conditions. The geographical distribution of kurtosis appears random, while skewness exhibits a distinct pattern: positive values predominantly occur in Central and Eastern Europe, whereas negative values are more common in Western Europe. The average spectral index value of the vertical coordinates across all stations is close to 1, indicating that they resemble pink noise, which is a nonstationary process. In this study, the spectral index is used to evaluate the stability of the stations’ vertical coordinates. A lower index (between 0 and 1) signifies greater stability, while a higher index (above 1) indicates lower stability. Here, stability refers to the temporal consistency of the mean value, which is of fundamental importance in geodesy.