distr6 (version 1.3.6)

Frechet: Frechet Distribution Class

Description

Mathematical and statistical functions for the Frechet distribution, which is commonly used as a special case of the Generalised Extreme Value distribution.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Frechet$new(shape = 1, scale = 1, minimum = 0, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
shape	numeric	shape parameter.
scale	numeric	scale parameter.
minimum	numeric	location parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Frechet distribution is parameterised with shape, scale as positive numerics and minimum as a numeric.

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 Frechet distribution parameterised with shape, \(\alpha\), scale, \(\beta\), and minimum, \(\gamma\), is defined by the pdf, $$f(x) = (\alpha/\beta)((x-\gamma)/\beta)^{-1-\alpha}exp(-(x-\gamma)/\beta)^{-\alpha}$$ for \(\alpha, \beta \epsilon R^+\) and \(\gamma \epsilon R\).

The distribution is supported on \(x > \gamma\).

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

Also known as the Inverse Weibull distribution.

References

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

See Also

listDistributions for all available distributions. Gumbel and Weibull for other special cases of the generalized extreme value distribution. CoreStatistics for numerical results.

Examples

# NOT RUN {
x = Frechet$new(shape = 2, scale = 3, minimum = 6)

# Update parameters
x$setParameterValue(shape = 3)
x$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)

# }