Hypergeometric | R Documentation |

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.

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,…}*, *n, K = {0,1,2,…,N}* and *C(a,b)* is the combination (or binomial coefficient) function.

Returns an R6 object inheriting from class SDistribution.

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

Hyper(size = 50, successes = 5, draws = 10)

N/A

N/A

`distr6::Distribution`

-> `distr6::SDistribution`

-> `Hypergeometric`

`name`

Full name of distribution.

`short_name`

Short name of distribution for printing.

`description`

Brief description of the distribution.

`packages`

Packages required to be installed in order to construct the distribution.

`properties`

Returns distribution properties, including skewness type and symmetry.

`new()`

Creates a new instance of this R6 class.

Hypergeometric$new( size = NULL, successes = NULL, failures = NULL, draws = NULL, decorators = NULL )

`size`

`(integer(1))`

Population size. Defined on positive Naturals.`successes`

`(integer(1))`

Number of population successes. Defined on positive Naturals.`failures`

`(integer(1))`

Number of population failures.`failures = size - successes`

. If given then`successes`

is ignored. Defined on positive Naturals.`draws`

`(integer(1))`

Number of draws from the distribution, defined on the positive Naturals.`decorators`

`(character())`

Decorators to add to the distribution during construction.

`mean()`

The arithmetic mean of a (discrete) probability distribution X is the expectation

*E_X(X) = ∑ p_X(x)*x*

with an integration analogue for continuous distributions.

Hypergeometric$mean(...)

`...`

Unused.

`mode()`

The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).

Hypergeometric$mode(which = "all")

`which`

`(character(1) | numeric(1)`

Ignored if distribution is unimodal. Otherwise`"all"`

returns all modes, otherwise specifies which mode to return.

`variance()`

The variance of a distribution is defined by the formula

*var_X = E[X^2] - E[X]^2*

where *E_X* is the expectation of distribution X. If the distribution is multivariate the
covariance matrix is returned.

Hypergeometric$variance(...)

`...`

Unused.

`skewness()`

The skewness of a distribution is defined by the third standardised moment,

*sk_X = E_X[((x - μ)/σ)^3]*

where *E_X* is the expectation of distribution X, *μ* is the mean of the
distribution and *σ* is the standard deviation of the distribution.

Hypergeometric$skewness(...)

`...`

Unused.

`kurtosis()`

The kurtosis of a distribution is defined by the fourth standardised moment,

*k_X = E_X[((x - μ)/σ)^4]*

where *E_X* is the expectation of distribution X, *μ* is the mean of the
distribution and *σ* is the standard deviation of the distribution.
Excess Kurtosis is Kurtosis - 3.

Hypergeometric$kurtosis(excess = TRUE, ...)

`excess`

`(logical(1))`

If`TRUE`

(default) excess kurtosis returned.`...`

Unused.

`setParameterValue()`

Sets the value(s) of the given parameter(s).

Hypergeometric$setParameterValue( ..., lst = list(...), error = "warn", resolveConflicts = FALSE )

`...`

`ANY`

Named arguments of parameters to set values for. See examples.`lst`

`(list(1))`

Alternative argument for passing parameters. List names should be parameter names and list values are the new values to set.`error`

`(character(1))`

If`"warn"`

then returns a warning on error, otherwise breaks if`"stop"`

.`resolveConflicts`

`(logical(1))`

If`FALSE`

(default) throws error if conflicting parameterisations are provided, otherwise automatically resolves them by removing all conflicting parameters.

`clone()`

The objects of this class are cloneable with this method.

Hypergeometric$clone(deep = FALSE)

`deep`

Whether to make a deep clone.

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

Other discrete distributions:
`Bernoulli`

,
`Binomial`

,
`Categorical`

,
`Degenerate`

,
`DiscreteUniform`

,
`EmpiricalMV`

,
`Empirical`

,
`Geometric`

,
`Logarithmic`

,
`Matdist`

,
`Multinomial`

,
`NegativeBinomial`

,
`WeightedDiscrete`

Other univariate distributions:
`Arcsine`

,
`Bernoulli`

,
`BetaNoncentral`

,
`Beta`

,
`Binomial`

,
`Categorical`

,
`Cauchy`

,
`ChiSquaredNoncentral`

,
`ChiSquared`

,
`Degenerate`

,
`DiscreteUniform`

,
`Empirical`

,
`Erlang`

,
`Exponential`

,
`FDistributionNoncentral`

,
`FDistribution`

,
`Frechet`

,
`Gamma`

,
`Geometric`

,
`Gompertz`

,
`Gumbel`

,
`InverseGamma`

,
`Laplace`

,
`Logarithmic`

,
`Logistic`

,
`Loglogistic`

,
`Lognormal`

,
`Matdist`

,
`NegativeBinomial`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

,
`WeightedDiscrete`

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