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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