ShiftedLoglogistic: Shifted Log-Logistic Distribution Class
In distr6: The Complete R6 Probability Distributions Interface
ShiftedLoglogistic R Documentation
Shifted Log-Logistic Distribution Class
Description
Mathematical and statistical functions for the Shifted Log-Logistic distribution, which
is commonly used in survival analysis for its non-monotonic hazard as well as in economics, a generalised variant of Loglogistic.
Details
The Shifted Log-Logistic distribution parameterised with shape, β, scale, α, and location, γ, is defined by the pdf,
f(x) = (β/α)((x-γ)/α)^{β-1}(1 + ((x-γ)/α)^β)^{-2}
for α, β > 0 and γ >= 0.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the non-negative Reals.
Default Parameterisation
ShiftLLogis(scale = 1, shape = 1, location = 0)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> ShiftedLoglogistic
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
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Inherited methods
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Method new()
Creates a new instance of this R6 class.
Usage
ShiftedLoglogistic$new(
scale = NULL,
shape = NULL,
location = NULL,
rate = NULL,
decorators = NULL
)
Arguments
scalenumeric(1))
Scale parameter of the distribution, defined on the positive Reals. scale = 1/rate.
If provided rate is ignored.
shape(numeric(1))
Shape parameter, defined on the positive Reals.
location(numeric(1))
Location parameter, defined on the Reals.
rate(numeric(1))
Rate parameter of the distribution, defined on the positive Reals.
decorators(character())
Decorators to add to the distribution during construction.
Method mean()
The arithmetic mean of a (discrete) probability distribution X is the expectation
E_X(X) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Usage
ShiftedLoglogistic$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
ShiftedLoglogistic$mode(which = "all")
Arguments
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
Method median()
Returns the median of the distribution. If an analytical expression is available
returns distribution median, otherwise if symmetric returns self$mean, otherwise
returns self$quantile(0.5).
Usage
ShiftedLoglogistic$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
ShiftedLoglogistic$variance(...)
Arguments
...Unused.
Method pgf()
The probability generating function is defined by
pgf_X(z) = E_X[exp(z^x)]
where X is the distribution and E_X is the expectation of the distribution X.
Usage
ShiftedLoglogistic$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
ShiftedLoglogistic$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,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
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,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
distr6 documentation built on March 28, 2022, 1:05 a.m.
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| ShiftedLoglogistic | R Documentation |
Shifted Log-Logistic Distribution Class
Description
Mathematical and statistical functions for the Shifted Log-Logistic distribution, which is commonly used in survival analysis for its non-monotonic hazard as well as in economics, a generalised variant of Loglogistic.
Details
The Shifted Log-Logistic distribution parameterised with shape, β, scale, α, and location, γ, is defined by the pdf,
f(x) = (β/α)((x-γ)/α)^{β-1}(1 + ((x-γ)/α)^β)^{-2}
for α, β > 0 and γ >= 0.
Value
Returns an R6 object inheriting from class SDistribution.
Distribution support
The distribution is supported on the non-negative Reals.
Default Parameterisation
ShiftLLogis(scale = 1, shape = 1, location = 0)
Omitted Methods
N/A
Also known as
N/A
Super classes
distr6::Distribution -> distr6::SDistribution -> ShiftedLoglogistic
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages required to be installed in order to construct the distribution.
Active bindings
propertiesReturns distribution properties, including skewness type and symmetry.
Methods
Public methods
Inherited methods
Method new()
Creates a new instance of this R6 class.
Usage
ShiftedLoglogistic$new( scale = NULL, shape = NULL, location = NULL, rate = NULL, decorators = NULL )
Arguments
scalenumeric(1))
Scale parameter of the distribution, defined on the positive Reals.scale = 1/rate. If providedrateis ignored.shape(numeric(1))
Shape parameter, defined on the positive Reals.location(numeric(1))
Location parameter, defined on the Reals.rate(numeric(1))
Rate parameter of the distribution, defined on the positive Reals.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) = ∑ p_X(x)*x
with an integration analogue for continuous distributions.
Usage
ShiftedLoglogistic$mean(...)
Arguments
...Unused.
Method mode()
The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Usage
ShiftedLoglogistic$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
ShiftedLoglogistic$median()
Method variance()
The variance of a distribution is defined by the formula
var_X = E[X^2] - E[X]^2
where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.
Usage
ShiftedLoglogistic$variance(...)
Arguments
...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
ShiftedLoglogistic$pgf(z, ...)
Arguments
z(integer(1))
z integer to evaluate probability generating function at....Unused.
Method clone()
The objects of this class are cloneable with this method.
Usage
ShiftedLoglogistic$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,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
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,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
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