The maximum negative hypergeometric distribution

Daniel Zelterman

The maximum negative hypergeometric distribution

Statistics Theory 2018-02-28 v1 Methodology Statistics Theory

Authors: Daniel Zelterman

Abstract

An urn contains a known number of balls of two different colors. We describe the random variable counting the smallest number of draws needed in order to observe at least $\,c\,$ of both colors when sampling without replacement for a pre-specified value of $\,c=1,2,\ldots\,$ . This distribution is the finite sample analogy to the maximum negative binomial distribution described by Zhang, Burtness, and Zelterman (2000). We describe the modes, approximating distributions, and estimation of the contents of the urn.

Keywords

urn models probability distribution

Cite

@article{arxiv.1802.09673,
  title  = {The maximum negative hypergeometric distribution},
  author = {Daniel Zelterman},
  journal= {arXiv preprint arXiv:1802.09673},
  year   = {2018}
}

Comments

25 pages, 6 figures; 2 tables

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