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.

## 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.

## Distribution support

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

## Default Parameterisation

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

N/A

N/A

## References

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

Other discrete distributions: Arrdist, Bernoulli, Binomial, Categorical, Degenerate, DiscreteUniform, EmpiricalMV, Empirical, Geometric, Logarithmic, Matdist, Multinomial, NegativeBinomial, WeightedDiscrete

Other univariate distributions: Arcsine, Arrdist, 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

## Super classes

distr6::Distribution -> distr6::SDistribution -> Hypergeometric

## Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

alias

Alias of the distribution.

packages

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

## Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

## Methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

#### Arguments

...

Unused.

### Method 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).

#### Arguments

...

Unused.

### Method skewness()

The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ where $$E_X$$ is the expectation of distribution X, $$\mu$$ is the mean of the distribution and $$\sigma$$ is the standard deviation of the distribution.

#### Arguments

excess

(logical(1))
If TRUE (default) excess kurtosis returned.

...

Unused.

### Method setParameterValue()

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

#### Arguments

deep

Whether to make a deep clone.