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.
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}
}