The sequential procedure of allocating particles is considered. Particles are successively thrown, independently and uniformly, in N given cells labelled 1, . . . , N. It is assumed that before the beginning of the trials for cell j a level ι/j, j = 1, . . . , TV, is settled, so that 1/1, . . . , ι/w are independent identically distributed (i.i.d.) integer-valued random variables (r.v.). The trials continue until k cells appear for the first time, whose frequencies (the number of particles in the cells) are not less than the corresponding levels. Decomposable statistics (d.s.) are studied, where g is a function of the integer argument and rjj is the frequency of the j'-th cell at the stopping moment. The general method of r.v. L^k studying is proposed, which reduces this problem to examining the sums of conditionally independent r.v. With this method it is possible to obtain a rather complete description of the limit distributions of d.s. in an equiprobable scheme as TV' -» oo and the parameter k varies.
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