English

On the expected number of different records in a random sample

Probability 2012-09-21 v1

Abstract

Given a discrete distribution, an interesting problem is to determine the minimum size of a random sample drawn from this distribution, in order to observe a given number of different records. This problem is related with many applied problems, like the Heaps' Law in linguistics and the classical Coupon-collector's problem. In this note we are able to compute theoretically the expected size of such a sample and we provide an approximation strategy in the case of the Mandelbrot distribution.

Keywords

Cite

@article{arxiv.1209.4592,
  title  = {On the expected number of different records in a random sample},
  author = {Marco Ferrante and Nadia Frigo},
  journal= {arXiv preprint arXiv:1209.4592},
  year   = {2012}
}
R2 v1 2026-06-21T22:08:36.197Z