In statistical analysis of discrete sequences, the problem often arises of testing the hypothesis H0 that the given sequence is obtained from a scheme of independent trials with N outcomes whose probabilities are q (qa, qz, ", qr) against the competing composite hypothesis H ={H(p)}, in which it is still assumed that the trials are independent and homogeneous, but where the probabilities p (pa, p, ., pu) of the corresponding trials are left arbitrary. A rather well developed theory is available for the case where the number of possible outcomes N is finite or whose growth, as the number of trials n increases, is such that the quantity a min np,, also increases without limit.
A new scheme of allocating particles with reflection is considered. For one variant of this scheme we present some exact and asymptotic results on the waiting time until all or almost all cells are occupied.
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