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Mathematical and statistical functions for the Frechet distribution, which is commonly used as a special case of the Generalised Extreme Value distribution.
Returns an R6 object inheriting from class SDistribution.
Frechet$new(shape = 1, scale = 1, minimum = 0, decorators = NULL, verbose = FALSE)
Argument | Type | Details |
shape |
numeric | shape parameter. |
scale |
numeric | scale parameter. |
minimum |
numeric | location parameter. |
decorators
Decorator
decorators to add functionality. See details.
The Frechet distribution is parameterised with shape
, scale
as positive numerics and minimum
as a numeric.
Variable | Return |
name |
Name of distribution. |
short_name |
Id of distribution. |
description |
Brief description of distribution. |
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 |
The Frechet distribution parameterised with shape,
The distribution is supported on
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.
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
listDistributions
for all available distributions. Gumbel
and Weibull
for other special cases of the generalized extreme value distribution. CoreStatistics
for numerical results.
# 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)
# }
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