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.

Returns an R6 object inheriting from class SDistribution.

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 \(n = {1,2,\ldots}\).

The distribution is supported on \(\sum x_i = N\).

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

`cdf`

and `quantile`

are
omitted as no closed form analytic expression could be found, decorate with `FunctionImputation`

for a numerical imputation.

N/A

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`

`distr6::Distribution`

-> `distr6::SDistribution`

-> `Multinomial`

`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.

`properties`

Returns distribution properties, including skewness type and symmetry.

`distr6::Distribution$cdf()`

`distr6::Distribution$confidence()`

`distr6::Distribution$correlation()`

`distr6::Distribution$getParameterValue()`

`distr6::Distribution$iqr()`

`distr6::Distribution$liesInSupport()`

`distr6::Distribution$liesInType()`

`distr6::Distribution$median()`

`distr6::Distribution$parameters()`

`distr6::Distribution$pdf()`

`distr6::Distribution$prec()`

`distr6::Distribution$print()`

`distr6::Distribution$quantile()`

`distr6::Distribution$rand()`

`distr6::Distribution$stdev()`

`distr6::Distribution$strprint()`

`distr6::Distribution$summary()`

`distr6::Distribution$workingSupport()`

`new()`

Creates a new instance of this R6 class.

`Multinomial$new(size = NULL, probs = NULL, decorators = NULL)`

`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.

`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.

`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.

`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.

`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.

`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.

`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.

`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.

`setParameterValue()`

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

```
Multinomial$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.