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Poisson randomization in occupancy problems

1983; Elsevier BV; Volume: 94; Issue: 1 Linguagem: Inglês

10.1016/0022-247x(83)90010-0

1096-0813

Mauro Cerasoli,

Bayesian Methods and Mixture Models

In occupancy problems we randomize the number of balls with a Poisson process of intensity α. Thus some classical formulas are very easily demonstrated and generalized with the aid of inclusion-exclusion principle. Then we give a general theorem to calculate the distributions and moments of particular random variables or waiting times when infinite balls are considered. This theorem can be applied to the well-known birthday and coupon collectors problems.