Gumbel: Gumbel Distribution Class

Description

Mathematical and statistical functions for the Gumbel distribution, which is commonly used to model the maximum (or minimum) of a number of samples of different distributions, and is a special case of the Generalised Extreme Value distribution.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Gumbel$new(location = 0, scale = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

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

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Gumbel distribution is parameterised with location as a numeric and scale as a positive 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 Gumbel distribution parameterised with location, $\mu$, and scale, $\beta$, is defined by the pdf, $$f(x) = exp(-(z + exp(-z)))/\beta$$ for $z = (x-\mu)/\beta$, $\mu \epsilon R$ and $\beta > 0$.

The distribution is supported on the Reals.

Apery's Constant to 16 significant figures is used in the skewness calculation. The gammaz function from the pracma package is used in the cf to allow complex inputs.

References

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

Examples

Run this code

# NOT RUN {
x = Gumbel$new(location = 2, scale = 5)

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

# }

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