A unique parabolic relation is observed to link skewness and kurtosis of density fluctuation signals, measured over the whole cross-section of the simple toroidal device TORPEX for a broad range of experimental conditions. This relationship is also valid for density fluctuation signals measured in the scrape-off layer of the TCV tokamak. All the probability density functions (PDFs) of the measured signals, including those characterized by a negative skewness, are universally described by a special case of the beta distribution. In TORPEX, fluctuations in the drift-interchange frequency range are necessary and sufficient to assure that PDFs can be described by this specific beta distribution. For a more detailed plasma scenario, it is shown that electron temperature and plasma potential fluctuations have different statistical properties compared with the density.