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`



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.

Examples

Run this code

# 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)

# }

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