distr6 (version 1.4.8)

Weibull: Weibull Distribution Class

Description

Mathematical and statistical functions for the Weibull distribution, which is commonly used in survival analysis as it satisfies both PH and AFT requirements.

Value

Returns an R6 object inheriting from class SDistribution.

Super classes

distr6::Distribution -> distr6::SDistribution -> Weibull

Public fields

name

Full name of distribution.

short_name

Short name of distribution for printing.

description

Brief description of the distribution.

packages

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

Methods

Public methods

• Weibull$new()

• Weibull$mean()

• Weibull$mode()

• Weibull$median()

• Weibull$variance()

• Weibull$skewness()

• Weibull$kurtosis()

• Weibull$entropy()

• Weibull$pgf()

• Weibull$setParameterValue()

• Weibull$clone()

• distr6::Distribution$cdf()

• 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$stdev()

• distr6::Distribution$strprint()

• distr6::Distribution$summary()

• distr6::Distribution$workingSupport()

Method new()

Creates a new instance of this R6 class.

Usage

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

Arguments

shape

(numeric(1)) Shape parameter, defined on the positive Reals.

scale

(numeric(1)) Scale parameter, defined on the positive Reals.

altscale

(numeric(1)) Alternative scale parameter, if given then scale is ignored. altscale = scale^-shape.

decorators

(character()) Decorators to add to the distribution during construction.

Method mean()

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

Usage

Weibull$mean(...)

Arguments

...

Unused.

Method 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).

Usage

Weibull$mode(which = "all")

Arguments

which

(character(1) | numeric(1) Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies which mode to return.

Method 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).

Usage

Weibull$median()

Method variance()

The variance of a distribution is defined by the formula $$va{r}_X=E[X^2]-E[X{]}^2$$ where $E_X$ is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

Usage

Weibull$variance(...)

Arguments

...

Unused.

Method skewness()

The skewness of a distribution is defined by the third standardised moment, $$s{k}_X=E_X[{\frac{x-\mu }{\sigma }}^3]$$ 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.

Usage

Weibull$skewness(...)

Arguments

...

Unused.

Method 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.

Usage

Weibull$kurtosis(excess = TRUE, ...)

Arguments

excess

(logical(1)) If TRUE (default) excess kurtosis returned.

...

Unused.

Method 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.

Usage

Weibull$entropy(base = 2, ...)

Arguments

base

(integer(1)) Base of the entropy logarithm, default = 2 (Shannon entropy)

...

Unused.

Method pgf()

The probability generating function is defined by $$pg{f}_X(z)=E_X[exp(z^x)]$$ where X is the distribution and $E_X$ is the expectation of the distribution X.

Usage

Weibull$pgf(z, ...)

Arguments

z

(integer(1)) z integer to evaluate probability generating function at.

...

Unused.

Method setParameterValue()

Sets the value(s) of the given parameter(s).

Usage

Weibull$setParameterValue(..., lst = NULL, error = "warn")

Arguments

...

ANY Named arguments of parameters to set values for. See examples.

lst

(list(1)) Alternative argument for passing parameters. List names should be parameter names and list values are the new values to set.

error

(character(1)) If "warn" then returns a warning on error, otherwise breaks if "stop".

Method clone()

The objects of this class are cloneable with this method.

Usage

Weibull$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

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.

References

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

See Also

Other continuous distributions: Arcsine, BetaNoncentral, Beta, Cauchy, ChiSquaredNoncentral, ChiSquared, Dirichlet, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Gompertz, Gumbel, InverseGamma, Laplace, Logistic, Loglogistic, Lognormal, MultivariateNormal, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald

Other univariate distributions: Arcsine, Bernoulli, BetaNoncentral, Beta, Binomial, Categorical, Cauchy, ChiSquaredNoncentral, ChiSquared, Degenerate, DiscreteUniform, Empirical, Erlang, Exponential, FDistributionNoncentral, FDistribution, Frechet, Gamma, Geometric, Gompertz, Gumbel, Hypergeometric, InverseGamma, Laplace, Logarithmic, Logistic, Loglogistic, Lognormal, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, WeightedDiscrete