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distr6 (version 1.5.2)

Loglogistic: Log-Logistic Distribution Class

Description

Mathematical and statistical functions for the Log-Logistic distribution, which is commonly used in survival analysis for its non-monotonic hazard as well as in economics.

Arguments

Value

Returns an R6 object inheriting from class SDistribution.

Distribution support

The distribution is supported on the non-negative Reals.

Default Parameterisation

LLogis(scale = 1, shape = 1)

Omitted Methods

N/A

Also known as

Also known as the Fisk distribution.

Super classes

distr6::Distribution -> distr6::SDistribution -> Loglogistic

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

Method new()

Creates a new instance of this R6 class.

Usage

Loglogistic$new(scale = NULL, shape = NULL, rate = NULL, decorators = NULL)

Arguments

scale

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

shape

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

rate

(numeric(1)) Alternate scale parameter, rate = 1/scale. If given then scale is ignored.

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

Loglogistic$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

Loglogistic$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

Loglogistic$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

Loglogistic$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

Loglogistic$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

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

Arguments

excess

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

...

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

Loglogistic$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

Loglogistic$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Details

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

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