A set of hypergeometric gaussian functions, with a consistent relation between age parameter and total size is proposed in the ultra high energy range (above 1 EeV) for electrons, and vertical equivalent muons (vem). This is an important step for a coherent interpretation of hybrid events recorded with both surface array and uorescence telescope. Observing that the extrapolation of the original cosmic ray primary spectrum derived from the size spectrum measured in the Akeno classical EAS array coincides with the spectrum measured recently by the Hires Stereo experiment , we point out a possible overestimation of the primary energy in inclined showers of the surface arrays like AGASA ; this circumstance gives more support to the GZK synopsis.