distr6 (version 1.3.6)

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 mode(which = "all") mode

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.

See Also

listDistributions for all available distributions. Binomial for a special case of the Multinomial distribution. FunctionImputation to numerically impute d/p/q/r.

Examples

# 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)

# }