Abstract
The definition of the Bernoulli sieve which is an infinite allocation scheme can be found on p. 1. Assuming that the number of balls to be allocated equals n (in other words, using a sample of size n from a uniform distribution on [0, 1]), denote by K n the number of occupied boxes and by M n the index of the last occupied box. Also, put L n : = M n − K n and note that L n equals the number of empty boxes within the occupancy range (i.e., we only count the empty boxes with indices not exceeding M n ).
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Iksanov, A. (2016). Application to the Bernoulli Sieve. In: Renewal Theory for Perturbed Random Walks and Similar Processes. Probability and Its Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49113-4_5
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