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Dakota Reference Manual
Version 6.15
Explore and Predict with Confidence
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Aleatory uncertain discrete variable - hypergeometric
This keyword is related to the topics:
Alias: none
Argument(s): INTEGER
Default: no hypergeometric uncertain variables
Child Keywords:
Required/Optional | Description of Group | Dakota Keyword | Dakota Keyword Description | |
---|---|---|---|---|
Required | total_population | Parameter for the hypergeometric probability distribution describing the size of the total population | ||
Required | selected_population | Distribution parameter for the hypergeometric distribution describing the size of the population subset of interest | ||
Required | num_drawn | Distribution parameter for the hypergeometric distribution describing the number of draws from a combined population | ||
Optional | initial_point | Initial values for variables | ||
Optional | descriptors | Labels for the variables |
The hypergeometric probability density is used when sampling without replacement from a total population of elements where
The density function for the hypergeometric distribution is given by:
where the three distribution parameters are:
In addition,
The hypergeometric is often described using an urn model. For example, say we have a total population containing N balls, and we know that m of the balls are white and the remaining balls are green. If we draw n balls from the urn without replacement, the hypergeometric distribution describes the probability of drawing x white balls.