Dakota Reference Manual  Version 6.15
Explore and Predict with Confidence
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selected_population


Distribution parameter for the hypergeometric distribution describing the size of the population subset of interest

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 the three distribution parameters are:

  • N is the total population
  • 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 drawn (e.g. number of balls drawn)

In addition,

  • x, the abscissa of the density function, indicates the number of successes (e.g. drawing a white ball)
  • $\left(\begin{array}{c}a\\b\end{array}\right)$ indicates a binomial coefficient ("a choose b")