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.

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 \(x > \gamma\).

Frec(shape = 1, scale = 1, minimum = 0)

N/A

Also known as the Inverse Weibull distribution.

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

Other continuous distributions:
`Arcsine`

,
`BetaNoncentral`

,
`Beta`

,
`Cauchy`

,
`ChiSquaredNoncentral`

,
`ChiSquared`

,
`Dirichlet`

,
`Erlang`

,
`Exponential`

,
`FDistributionNoncentral`

,
`FDistribution`

,
`Gamma`

,
`Gompertz`

,
`Gumbel`

,
`InverseGamma`

,
`Laplace`

,
`Logistic`

,
`Loglogistic`

,
`Lognormal`

,
`MultivariateNormal`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

Other univariate distributions:
`Arcsine`

,
`Arrdist`

,
`Bernoulli`

,
`BetaNoncentral`

,
`Beta`

,
`Binomial`

,
`Categorical`

,
`Cauchy`

,
`ChiSquaredNoncentral`

,
`ChiSquared`

,
`Degenerate`

,
`DiscreteUniform`

,
`Empirical`

,
`Erlang`

,
`Exponential`

,
`FDistributionNoncentral`

,
`FDistribution`

,
`Gamma`

,
`Geometric`

,
`Gompertz`

,
`Gumbel`

,
`Hypergeometric`

,
`InverseGamma`

,
`Laplace`

,
`Logarithmic`

,
`Logistic`

,
`Loglogistic`

,
`Lognormal`

,
`Matdist`

,
`NegativeBinomial`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

,
`WeightedDiscrete`

`distr6::Distribution`

-> `distr6::SDistribution`

-> `Frechet`

`name`

Full name of distribution.

`short_name`

Short name of distribution for printing.

`description`

Brief description of the distribution.

`alias`

Alias of the distribution.

`packages`

Packages required to be installed in order to construct the distribution.

`properties`

Returns distribution properties, including skewness type and symmetry.

`distr6::Distribution$cdf()`

`distr6::Distribution$confidence()`

`distr6::Distribution$correlation()`

`distr6::Distribution$getParameterValue()`

`distr6::Distribution$iqr()`

`distr6::Distribution$liesInSupport()`

`distr6::Distribution$liesInType()`

`distr6::Distribution$parameters()`

`distr6::Distribution$pdf()`

`distr6::Distribution$prec()`

`distr6::Distribution$print()`

`distr6::Distribution$quantile()`

`distr6::Distribution$rand()`

`distr6::Distribution$setParameterValue()`

`distr6::Distribution$stdev()`

`distr6::Distribution$strprint()`

`distr6::Distribution$summary()`

`distr6::Distribution$workingSupport()`

`new()`

Creates a new instance of this R6 class.

`Frechet$new(shape = NULL, scale = NULL, minimum = NULL, decorators = NULL)`

`mean()`

The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.

`mode()`

The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).

`median()`

Returns the median of the distribution. If an analytical expression is available
returns distribution median, otherwise if symmetric returns `self$mean`

, otherwise
returns `self$quantile(0.5)`

.

`variance()`

The variance of a distribution is defined by the formula $$var_X = E[X^2] - E[X]^2$$ where \(E_X\) is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

`skewness()`

The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution.

`kurtosis()`

The kurtosis of a distribution is defined by the fourth standardised moment, $$k_X = E_X[\frac{x - \mu}{\sigma}^4]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.

`entropy()`

The entropy of a (discrete) distribution is defined by $$- \sum (f_X)log(f_X)$$ where \(f_X\) is the pdf of distribution X, with an integration analogue for continuous distributions.

`pgf()`

The probability generating function is defined by $$pgf_X(z) = E_X[exp(z^x)]$$ where X is the distribution and \(E_X\) is the expectation of the distribution X.