Multinomial: Multinomial Distribution Class

Description

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.

Constructor

Multinomial$new(size = 10, probs = c(0.5, 0.5), decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`size`	numeric	number of trials. See details.
`probs`	numeric	vector of probabilities. See details.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Multinomial distribution is parameterised with size as a positive whole number and probs as a vector of numerics between 0 and 1. The length of the probability vector, $K$, tells the constructor how many arguments to expect to be passed to the maths/stats methods. The probability vector is automatically normalised with $$probs = probs/sum(probs)$$.

Public Variables

Variable	Return
`name`	Name of distribution.
`short_name`	Id of distribution.
`description`	Brief description of distribution.

Public Methods

Accessor Methods	Link
`decorators()`	`decorators`
`traits()`	`traits`
`valueSupport()`	`valueSupport`
`variateForm()`	`variateForm`
`type()`	`type`
`properties()`	`properties`
`support()`	`support`
`symmetry()`	`symmetry`
`sup()`	`sup`
`inf()`	`inf`
`dmax()`	`dmax`
`dmin()`	`dmin`
`skewnessType()`	`skewnessType`
`kurtosisType()`	`kurtosisType`



Statistical Methods	Link
`pdf(x1, ..., log = FALSE, simplify = TRUE)`	`pdf`
`cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`cdf`
`quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`quantile.Distribution`
`rand(n, simplify = TRUE)`	`rand`
`mean()`	`mean.Distribution`
`variance()`	`variance`
`stdev()`	`stdev`
`prec()`	`prec`
`cor()`	`cor`
`skewness()`	`skewness`
`kurtosis(excess = TRUE)`	`kurtosis`
`entropy(base = 2)`	`entropy`
`mgf(t)`	`mgf`
`cf(t)`	`cf`
`pgf(z)`	`pgf`
`median()`	`median.Distribution`
`iqr()`	`iqr`



Parameter Methods	Link
`parameters(id)`	`parameters`
`getParameterValue(id, error = "warn")`	`getParameterValue`
`setParameterValue(..., lst = NULL, error = "warn")`	`setParameterValue`



Validation Methods	Link
`liesInSupport(x, all = TRUE, bound = FALSE)`	`liesInSupport`
`liesInType(x, all = TRUE, bound = FALSE)`	`liesInType`



Representation Methods	Link
`strprint(n = 2)`	`strprint`
`print(n = 2)`	`print`
`summary(full = T)`	`summary.Distribution`

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 $n = {1,2,\ldots}$.

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

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

References

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

Examples

Run this code

# NOT RUN {
x <- Multinomial$new(size = 5, probs = c(0.1, 0.5, 0.9)) # Automatically normalised

# Update parameters
x$setParameterValue(size = 10)
# Number of categories cannot be changed after construction
x$setParameterValue(probs = c(1,2,3))
x$parameters()

# d/p/q/r
# Note the difference from R stats
x$pdf(4, 4, 2)
# This allows vectorisation:
x$pdf(c(1,4),c(2,4),c(7,2))

x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }

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