distr6 (version 1.5.6)

ShiftedLoglogistic: 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.

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

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

• ShiftedLoglogistic$new()

• ShiftedLoglogistic$mean()

• ShiftedLoglogistic$mode()

• ShiftedLoglogistic$median()

• ShiftedLoglogistic$variance()

• ShiftedLoglogistic$pgf()

• ShiftedLoglogistic$setParameterValue()

• ShiftedLoglogistic$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

ShiftedLoglogistic$new(
  scale = NULL,
  shape = NULL,
  location = NULL,
  rate = NULL,
  decorators = NULL
)

Arguments

scale

numeric(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 $$E_X(X) = \sum p_X(x)*x$$ 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 setParameterValue()

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

Usage

ShiftedLoglogistic$setParameterValue(
  ...,
  lst = NULL,
  error = "warn",
  resolveConflicts = FALSE
)

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".

resolveConflicts

(logical(1)) If FALSE (default) throws error if conflicting parameterisations are provided, otherwise automatically resolves them by removing all conflicting parameters.

Method clone()

The objects of this class are cloneable with this method.

Usage

ShiftedLoglogistic$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

The Shifted Log-Logistic distribution parameterised with shape, \(\beta\), scale, \(\alpha\), and location, \(\gamma\), is defined by the pdf, $$f(x) = (\beta/\alpha)((x-\gamma)/\alpha)^{\beta-1}(1 + ((x-\gamma)/\alpha)^\beta)^{-2}$$ for \(\alpha, \beta > 0\) and \(\gamma >= 0\).

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, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete