About invariants structures of series and criteria of accident of consecutive sample

In article are considered laws of formation of series, in consecutive sample of a continuous random variable by positions of individual values concerning the central line and attitudes of the order between the next values. The opportunity of generalization of results of the theory of Mizes-Feller's recurrent events for series, is shown by attitudes of the order. The general view of making function of time of returning and asymptotic estimations of numerical characteristics of number of series of the fixed length for series of the specified type is received. On the basis of the established laws of distribution are revealed инварианты structures of series, criteria of accident of sample are formulated and their experimental check by statistical modelling by a method of Monte-Carlo is lead.