What is a Hypergeometric Distribution?

A hypergeometric distribution is a discrete random sampling distribution. The sampling is from a series of n trials, from a finite population of size N. Each trial may have outcomes which fall into one of two classifications.

Calculations

The probability of exactly r occurrences in n trails may be calculated by the following hypergeometric formula.

HyperGeometricCalc

  • r is the number of occurrences,
  • Npi is the number of occurrences in the Population,
  • N is the Population size, and
  • n is the sample size.

Other Properties

The limit of the hypergeometric distribution, as the ration of n/N goes toward zero, yields a Binomial Distribution.

Example

Here is an example hypergeometric distribution, assuming a sample size of 10, a population of size 100, and a probability of occurrence of 0.15. The probability of observing no occurrences with a sample of size 10 from a population of size 100, with a probability of 0.15 is 0.1808.

Hypergeometric Distribution

     p = 0.1500     n = 10     N = 100
    np = 1.5000    Np = 15.0000

            Prob     Equal &     Equal &
   r        at r       Above       Below
   0      0.1808      1.0000      0.1808 |------------------
   1      0.3568      0.8192      0.5375 |-----------------------------------
   2      0.2919      0.4625      0.8295 |-----------------------------
   3      0.1297      0.1705      0.9592 |-------------
   4      0.0345      0.0408      0.9937 |---
   5      0.0057      0.0063      0.9994 |-
   6      0.0006      0.0006      1.0000 |
   7      0.0000      0.0000      1.0000 |
   8      0.0000      0.0000      1.0000 |
   9      0.0000      0.0000      1.0000 |
  10      0.0000      0.0000      1.0000 |