Dakota Reference Manual  Version 6.4
Large-Scale Engineering Optimization and Uncertainty Analysis
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selected_population


Distribution parameter for the hypergeometric distribution

Specification

Alias: none

Argument(s): INTEGERLIST

Description

The density function for the hypergeometric distribution is given by:

\[f(x) = \frac{\left(\begin{array}{c}m\\x\end{array}\right)\left(\begin{array}{c}{N-m}\\{n-x}\end{array}\right)}{\left(\begin{array}{c}N\\n\end{array}\right)}\]

where

  • N is the total population (e.g. the total number of balls in the urn)
  • m is the number of items in the selected population (e.g. the number of white balls in the full urn of N items)
  • n is the size of the sample (e.g. number of balls drawn)
  • x is the number of sucess (e.g. drawing a white ball)
  • $ \frac{a}{b}$ is a binomial coeffecient