A poisson limit law for a generalized birthday problem

Norbert Henze

Statistics & Probability Letters, 1998, vol. 39, issue 4, 333-336

Abstract: Balls are placed sequentially at random into n cells. Write Tn,c(m) for the number of balls needed until for the mth time a ball is placed into a cell already containing c - 1 balls, where m [greater-or-equal, slanted] 1 and c [greater-or-equal, slanted] 2 are fixed integers. For fixed t> 0, let Xn,c denote the number of cells containing at least c balls after the placement of kn = [n1-1/c · t] balls. It is shown that, as n --> [infinity], the limit distribution of Xn,c is Poisson with parameter tc/c! As a consequence, the limit law of n1-c(Tn,c(m))c/c! is a Gamma distribution.

Keywords: Sequential; occupancy; problem; General; birthday; problem; Coincidences; Inclusion-exclusion; principle (search for similar items in EconPapers)
Date: 1998
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Citations: View citations in EconPapers (1)

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