R: Biased Urn Model Distributions

BiasedUrn-package {BiasedUrn} | R Documentation

## Biased Urn Model Distributions

### Description

Statistical models of biased sampling in the form of univariate and multivariate noncentral hypergeometric distributions, including Wallenius' noncentral hypergeometric distribution and Fisher's noncentral hypergeometric distribution (also called extended hypergeometric distribution).

These are distributions that you can get when taking colored balls from an urn without replacement, with bias. The univariate distributions are used when there are two colors of balls. The multivariate distributions are used when there are more than two colors of balls.

The (central) univariate and multivariate hypergeometric distribution can be obtained by setting `odds` = 1.

Please see `vignette("UrnTheory")` for a definition of these distributions and how to decide which distribution to use in a specific case.

### Details

Package: | BiasedUrn
Type: | Package
Version: | 1.06
Date: | 2013-11-06
License: | GPL

Univariate functions in this package

| Wallenius' noncentral hypergeometric | Fisher's noncentral hypergeometric
Probability mass function | dWNCHypergeo | dFNCHypergeo
Cumulative distribution function | pWNCHypergeo | pFNCHypergeo
Quantile function | qWNCHypergeo | qFNCHypergeo
Random variate generation function | rWNCHypergeo | rFNCHypergeo
Calculate mean | meanWNCHypergeo | meanFNCHypergeo
Calculate variance | varWNCHypergeo | varFNCHypergeo
Calculate mode | modeWNCHypergeo | modeFNCHypergeo
Estimate odds from mean | oddsWNCHypergeo | oddsFNCHypergeo
Estimate number from mean and odds | numWNCHypergeo | numFNCHypergeo
Minimum x | minHypergeo | minHypergeo
Maximum x | maxHypergeo | maxHypergeo

Multivariate functions in this package

| Wallenius' noncentral hypergeometric | Fisher's noncentral hypergeometric
Probability mass function | dMWNCHypergeo | dMFNCHypergeo
Random variate generation function | rMWNCHypergeo | rMFNCHypergeo
Calculate mean | meanMWNCHypergeo | meanMFNCHypergeo
Calculate variance | varMWNCHypergeo | varMFNCHypergeo
Calculate mean and variance | momentsMWNCHypergeo | momentsMFNCHypergeo
Estimate odds from mean | oddsMWNCHypergeo | oddsMFNCHypergeo
Estimage number from mean and odds | numMWNCHypergeo | numMFNCHypergeo
Minimum x | minMHypergeo | minMHypergeo
Maximum x | maxMHypergeo | maxMHypergeo

### Note

The implementation cannot run safely in multiple threads simultaneously

### Author(s)

Agner Fog

Maintainer: Agner Fog <agner@agner.org>

### References

http://www.agner.org/random/

### See Also

`vignette("UrnTheory")`
`BiasedUrn-Univariate`.
`BiasedUrn-Multivariate`.
`dhyper`
`fisher.test`

### Examples

    dWNCHypergeo(12, 25, 32, 20, 2.5)

[Package BiasedUrn version 1.07 Index]