Approximation of individual and mean cascades with energies above the GZK cut-off

Approximation of individual cascades of giant energies is an essential part of energy determination methods for primary particles. Fluctuations of the cascades and their distribution shapes were investigated based on a sufficient number of MC simulated showers, as dependent on primary energy and zenith angle. Individual cascades were approximated with high accuracy using very simple formula with interpreted parameters. This formula is convenient for both processing experimental data and analytical investigation. The primary energy dependence of physically interpreted values of the mean cascade parameters is shown. The problems of correct description of individual and mean showers are discussed.