Mathematical and statistical functions for the Multinomial distribution, which is commonly used to extend the binomial distribution to multiple variables, for example to model the rolls of multiple dice multiple times.

## Value

Returns an R6 object inheriting from class SDistribution.

## Details

The Multinomial distribution parameterised with number of trials, $$n$$, and probabilities of success, $$p_1,...,p_k$$, is defined by the pmf, $$f(x_1,x_2,\ldots,x_k) = n!/(x_1! * x_2! * \ldots * x_k!) * p_1^{x_1} * p_2^{x_2} * \ldots * p_k^{x_k}$$ for $$p_i, i = {1,\ldots,k}; \sum p_i = 1$$ and $$n = {1,2,\ldots}$$.

## Distribution support

The distribution is supported on $$\sum x_i = N$$.

## Default Parameterisation

Multinom(size = 10, probs = c(0.5, 0.5))

## Omitted Methods

cdf and quantile are omitted as no closed form analytic expression could be found, decorate with FunctionImputation for a numerical imputation.

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, Hypergeometric, Logarithmic, Matdist, NegativeBinomial, WeightedDiscrete

Other multivariate distributions: Dirichlet, EmpiricalMV, MultivariateNormal

## Super classes

distr6::Distribution -> distr6::SDistribution -> Multinomial

## 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 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.

#### Arguments

...

Unused.

### Method 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.

#### Arguments

base

(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)

...

Unused.

### Method 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.

#### Arguments

t

(integer(1))
t integer to evaluate function at.

...

Unused.

### Method 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.

Multinomial$pgf(z, ...) #### Arguments z (integer(1)) z integer to evaluate probability generating function at. ... Unused. ### Method setParameterValue() Sets the value(s) of the given parameter(s). #### Usage Multinomial$setParameterValue(
...,
lst = list(...),
error = "warn",
resolveConflicts = FALSE
)

#### Arguments

...

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.

### Method clone()

The objects of this class are cloneable with this method.

#### Usage

Multinomial\$clone(deep = FALSE)

#### Arguments

deep

Whether to make a deep clone.