Empirical: Empirical Distribution Class

Description

Mathematical and statistical functions for the Empirical distribution, which is commonly used in sampling such as MCMC.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Empirical$new(samples, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`samples`	numeric	vector of observed samples.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Empirical distribution is parameterised with a vector of elements for the support set.

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 Empirical distribution is defined by the pmf, $$p(x) = \sum I(x = x_i) / k$$ for $x_i \epsilon R, i = 1,...,k$.

The distribution is supported on $x_1,...,x_k$.

Sampling from this distribution is performed with the sample function with the elements given as the support set and uniform probabilities. 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 {
x = Empirical$new(stats::runif(1000)*10)

# d/p/q/r
x$pdf(1:5)
x$cdf(1:5) # Assumes ordered in construction
x$quantile(0.42) # Assumes ordered in construction
x$rand(10)

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

summary(x)

# }

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