Standard Article

Occupancy Problem

Ecological Statistics

  1. Trent L. Mcdonald

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vao001.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Mcdonald, T. L. 2013. Occupancy Problem . Encyclopedia of Environmetrics. 4.

Author Information

  1. West Inc., Cheyenne, WY, USA

Publication History

  1. Published Online: 15 JAN 2013


The “occupancy problem” has also been called the “sequential occupancy problem” and the “coupon-collector's problem”. Although there exist many variations, one popular statement of the problem asks, “What is the probability that a set of n independent multinomial trials yield at least one member of y classes?” The answer to this question has direct application in many sampling situations, particularly when sampling for members of a population with certain characteristics (such as species members, members with defects, etc.). An answer to this question, under general probabilities of class membership, is given in this article through the occupancy probability mass function and cumulative mass function. This article also mentions the corresponding waiting-time question that asks how many multinomial trials need to be conducted (i.e. how large should n be) in order to have a certain chance of obtaining at least one member of y classes.


  • coupon collecter problem;
  • occupancy;
  • sampling