Mathematical and statistical functions for the Binomial distribution, which is commonly used to model the number of successes out of a number of independent trials.

Returns an R6 object inheriting from class SDistribution.

The Binomial distribution parameterised with number of trials, n, and probability of success, p, is defined by the pmf, $$f(x) = C(n, x)p^x(1-p)^{n-x}$$ for \(n = 0,1,2,\ldots\) and probability \(p\), where \(C(a,b)\) is the combination (or binomial coefficient) function.

The distribution is supported on \({0, 1,...,n}\).

Binom(size = 10, prob = 0.5)

N/A

N/A

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

Other discrete distributions:
`Bernoulli`

,
`Categorical`

,
`Degenerate`

,
`DiscreteUniform`

,
`EmpiricalMV`

,
`Empirical`

,
`Geometric`

,
`Hypergeometric`

,
`Logarithmic`

,
`Multinomial`

,
`NegativeBinomial`

,
`WeightedDiscrete`

Other univariate distributions:
`Arcsine`

,
`Bernoulli`

,
`BetaNoncentral`

,
`Beta`

,
`Categorical`

,
`Cauchy`

,
`ChiSquaredNoncentral`

,
`ChiSquared`

,
`Degenerate`

,
`DiscreteUniform`

,
`Empirical`

,
`Erlang`

,
`Exponential`

,
`FDistributionNoncentral`

,
`FDistribution`

,
`Frechet`

,
`Gamma`

,
`Geometric`

,
`Gompertz`

,
`Gumbel`

,
`Hypergeometric`

,
`InverseGamma`

,
`Laplace`

,
`Logarithmic`

,
`Logistic`

,
`Loglogistic`

,
`Lognormal`

,
`NegativeBinomial`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

,
`WeightedDiscrete`

`distr6::Distribution`

-> `distr6::SDistribution`

-> `Binomial`

`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.

`new()`

Creates a new instance of this R6 class.

Binomial$new(size = NULL, prob = NULL, qprob = NULL, decorators = NULL)

`size`

`(integer(1))`

Number of trials, defined on the positive Naturals.`prob`

`(numeric(1))`

Probability of success.`qprob`

`(numeric(1))`

Probability of failure. If provided then`prob`

is ignored.`qprob = 1 - prob`

.`decorators`

`(character())`

Decorators to add to the distribution during construction.

`mean()`

The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.

Binomial$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).

Binomial$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.

Binomial$variance(...)

`...`

Unused.

`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.

Binomial$skewness(...)

`...`

Unused.

`kurtosis()`

The kurtosis of a distribution is defined by the fourth standardised moment, $$k_X = E_X[\frac{x - \mu}{\sigma}^4]$$ 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. Excess Kurtosis is Kurtosis - 3.

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

`excess`

`(logical(1))`

If`TRUE`

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

Unused.

`entropy()`

The entropy of a (discrete) distribution is defined by $$- \sum (f_X)log(f_X)$$ where \(f_X\) is the pdf of distribution X, with an integration analogue for continuous distributions.

Binomial$entropy(base = 2, ...)

`base`

`(integer(1))`

Base of the entropy logarithm, default = 2 (Shannon entropy)`...`

Unused.

`mgf()`

The moment generating function is defined by $$mgf_X(t) = E_X[exp(xt)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.

Binomial$mgf(t, ...)

`t`

`(integer(1))`

t integer to evaluate function at.`...`

Unused.

`cf()`

The characteristic function is defined by $$cf_X(t) = E_X[exp(xti)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.

Binomial$cf(t, ...)

`t`

`(integer(1))`

t integer to evaluate function at.`...`

Unused.

`pgf()`

The probability generating function is defined by $$pgf_X(z) = E_X[exp(z^x)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.

Binomial$pgf(z, ...)

`z`

`(integer(1))`

z integer to evaluate probability generating function at.`...`

Unused.

`setParameterValue()`

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

Binomial$setParameterValue( ..., lst = NULL, 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.

Binomial$clone(deep = FALSE)

`deep`

Whether to make a deep clone.