Pareto: Pareto Distribution Class

Description

Mathematical and statistical functions for the Pareto distribution, which is commonly used in Economics to model the distribution of wealth and the 80-20 rule.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Pareto$new(shape = 1, scale = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`shape`	numeric	shape parameter.
`scale`	numeric	scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Pareto distribution is parameterised with shape and scale as positive numerics.

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 Pareto distribution parameterised with shape, $\alpha$, and scale, $\beta$, is defined by the pdf, $$f(x) = (\alpha\beta^\alpha)/(x^{\alpha+1})$$ for $\alpha, \beta > 0$.

The distribution is supported on $[\beta, \infty)$.

cf is omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

References

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

Examples

Run this code

# NOT RUN {
x = Pareto$new(shape = 2, scale = 1)

# Update parameters
x$setParameterValue(scale = 5.1)
x$parameters()

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

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

summary(x)

# }

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