Weibull: Weibull Distribution Class
In RaphaelS1/distr6: The Complete R6 Probability Distributions Interface
Weibull R Documentation
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.
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.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Positive Reals.
Default Parameterisation
Weibull(shape = 1, scale = 1)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> Weibull
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Methods
Public methods
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Inherited methods
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()
Method new()
Creates a new instance of this R6 class.
Usage
Weibull$new(shape = NULL, scale = NULL, altscale = NULL, decorators = NULL)
Arguments
shape(numeric(1))
Shape parameter, defined on the positive Reals.
scale(numeric(1))
Scale parameter, defined on the positive Reals.
altscale(numeric(1))
Alternative scale parameter, if given then scale is ignored.
altscale = scale^-shape.
decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = \sum p_X(x)*x
with an integration analogue for continuous distributions.
Usage
Weibull$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
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.
Usage
Weibull$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[\frac{x - \mu}{\sigma}^3]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Usage
Weibull$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
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
Weibull$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
Weibull$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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,
Arrdist,
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,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
WeightedDiscrete
RaphaelS1/distr6 documentation built on Feb. 24, 2024, 9:14 p.m.
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| Weibull | R Documentation |
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.
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.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the Positive Reals.
Default Parameterisation
Weibull(shape = 1, scale = 1)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> Weibull
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
aliasAlias of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Methods
Public methods
Inherited methods
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()
Method new()
Creates a new instance of this R6 class.
Usage
Weibull$new(shape = NULL, scale = NULL, altscale = NULL, decorators = NULL)
Arguments
shape(numeric(1))
Shape parameter, defined on the positive Reals.scale(numeric(1))
Scale parameter, defined on the positive Reals.altscale(numeric(1))
Alternative scale parameter, if given thenscaleis ignored.altscale = scale^-shape.decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = \sum p_X(x)*x
with an integration analogue for continuous distributions.
Usage
Weibull$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
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.
Usage
Weibull$variance(...)
Arguments
...Unused.
Method skewness()
The skewness of a distribution is defined by the third standardised moment,
sk_X = E_X[\frac{x - \mu}{\sigma}^3]
where E_X is the expectation of distribution X, \mu is the mean of the
distribution and \sigma is the standard deviation of the distribution.
Usage
Weibull$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$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- \sum (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for
continuous distributions.
Usage
Weibull$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
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
Weibull$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
Weibull$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
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,
Arrdist,
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,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
WeightedDiscrete
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