Weibull: Weibull Distribution Class

Description

Mathematical and statistical functions for the Weibull distribution, which is commonly used in survival analysis and is a special case of the Generalized Extreme Value distribution.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

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

Constructor Arguments

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

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Weibull distribution is parameterised with shape, scale, and altscale 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`



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

The distribution is supported on the Positive Reals.

mgf and cf are 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 {
# Different parameterisations
Weibull$new(shape = 1, scale = 2)
Weibull$new(shape = 2, altscale = 2)

x <- Weibull$new(shape = 2, scale = 3)

# Update parameters
x$setParameterValue(scale = 1)
x$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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