distr6 (version 1.3.6)

Categorical: Categorical Distribution Class

Description

Mathematical and statistical functions for the Categorical distribution, which is commonly used in classification supervised learning.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Categorical$new(..., probs, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
...	ANY	elements in the support Set. See details.
probs	numeric	vector of probabilities. See details.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Categorical distribution is parameterised with a series of elements for the support set and probs determining the probability of each category occurring. The length of the probability list should equal the number of elements. The probability vector is automatically normalised with $$probs = probs/sum(probs)$$ If no arguments are given, then defaults to one element '1' with probability one.

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 Categorical distribution parameterised with a given support set, \(x_1,...,x_k\), and respective probabilities, \(p_1,...,p_k\), is defined by the pmf, $$f(x_i) = p_i$$ for \(p_i, i = 1,\ldots,k; \sum p_i = 1\).

The distribution is supported on \(x_1,...,x_k\).

Only the mode, pdf, cdf, quantile and rand are available for this Distribution, all other methods return NaN. Sampling from this distribution is performed with the sample function with the elements given as the support set and the probabilities from the probs parameter. The cdf and quantile assumes that the elements are supplied in an indexed order (otherwise the results are meaningless).

References

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

See Also

listDistributions for all available distributions. sample for the sampling function.

Examples

# NOT RUN {
# Note probabilities are automatically normalised
x = Categorical$new("Bapple","Banana",2,probs=c(0.2,0.4,1))

# Only the probabilities can be changed and must the same length as in construction
x$setParameterValue(probs = c(0.1,0.2,0.7))

# d/p/q/r
x$pdf(c("Bapple", "Carrot", 1, 2))
x$cdf("Banana") # Assumes ordered in construction
x$quantile(0.42) # Assumes ordered in construction
x$rand(10)

# Statistics
x$mode()

summary(x)

# }