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The problem of description of characteristic of UHE cascades with account physical fluctuations and accuracy of measuring process is discussed. To estimate energy and kind of the primary particle the longitudinal development of an individual extensive air shower should be accurately described: both the specific form of longitudinal development and errors of measurements should be taken into account. It is suggested to use function form of Acxp(-(x-c)7(a(x-c)+2b*)) which is a generalization of the normal law as a distribution function of measuring errors. The maximum likelihood method has been applied to find out the parameters of an approximation. The values of parameters for the event observed by Fly’s Eye in October 1991 have been found.