Аннотация:Investigation of rare, difficulty registered (1 event per 1km^2/sr in a year at energy E 5•10^18 eV) cascades of ultra high energy leads, as rule, to operating with incomplete data, which have systematic, stochastic and statistical errors order of 10%. Before obtained properties of form A*exp(-(x-c)^2/(a(x-c)+2b^2)) and specific methods of approximation gave ability to mean an individual cascade as concrete realization of interpreted probabilistic parameters; to create the approximation of individual showers, and to detect less fluctuating parameters.
The atmospheric depth of maximum of cascade is investigated and its full description is presented by the created distribution function. Results undergo to analysis, checking, comparisons with ones obtained other methods and experimental data. The increase of the statistic UHE events points to usefulness the formal apparatus of distribution functions as instrument of the investigation even for incomplete and low quality data.