distr6 (version 1.3.6)

Hypergeometric: Hypergeometric Distribution Class

Description

Mathematical and statistical functions for the Hypergeometric distribution, which is commonly used to model the number of successes out of a population containing a known number of possible successes, for example the number of red balls from an urn or red, blue and yellow balls.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Hypergeometric$new(size = 10, successes = 5, failures = NULL, draws = 2, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
size	numeric	population size.
successes	numeric	number of population successes.
failures	numeric	number of population failures.
draws	numeric	number of draws.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Hypergeometric distribution is parameterised with size and draws as positive whole numbers, and either successes or failures as positive whole numbers. These are related via, $$failures = size - successes$$ If failures is given then successes is ignored.

Public Variables

Variable	Return
name	Name of distribution.
short_name	Id of distribution.
description	Brief description of distribution.

Public Methods

Accessor Methods	Link
decorators	decorators
traits	traits
valueSupport	valueSupport
variateForm	variateForm
type	type
properties	properties
support	support
symmetry	symmetry
sup	sup
inf	inf
dmax	dmax
dmin	dmin
skewnessType	skewnessType
kurtosisType	kurtosisType

Statistical Methods Link pdf(x1, ..., log = FALSE, simplify = TRUE) pdf cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) cdf quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) quantile.Distribution rand(n, simplify = TRUE) rand mean() mean.Distribution variance() variance stdev() stdev prec() prec cor() cor skewness() skewness kurtosis(excess = TRUE) kurtosis entropy(base = 2) entropy mgf(t) mgf cf(t) cf pgf(z) pgf median() median.Distribution iqr() iqr mode(which = "all") mode

Parameter Methods Link parameters(id) parameters getParameterValue(id, error = "warn") getParameterValue setParameterValue(..., lst = NULL, error = "warn") setParameterValue

Validation Methods Link liesInSupport(x, all = TRUE, bound = FALSE) liesInSupport liesInType(x, all = TRUE, bound = FALSE) liesInType

Representation Methods Link strprint(n = 2) strprint print(n = 2) print summary(full = T) summary.Distribution

Details

The Hypergeometric distribution parameterised with population size, \(N\), number of possible successes, \(K\), and number of draws from the distribution, \(n\), is defined by the pmf, $$f(x) = C(K, x)C(N-K,n-x)/C(N,n)$$ for \(N = \{0,1,2,\ldots\}\), \(n, K = \{0,1,2,\ldots,N\}\) and \(C(a,b)\) is the combination (or binomial coefficient) function.

The distribution is supported on \(\{max(0, n + K - N),...,min(n,K)\}\).

mgf and cf are omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

See Also

listDistributions for all available distributions. CoreStatistics for numerical results.

Examples

# NOT RUN {
Hypergeometric$new(size = 10, successes = 7, draws = 5)
Hypergeometric$new(size = 10, failures = 3, draws = 5)

# Default is size = 50, successes = 5, draws = 10
x = Hypergeometric$new(verbose = TRUE)

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(failures = 10)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }