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.

Examples

Run this code

# 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)

# }

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