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.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on the non-negative Reals.
LLogis(scale = 1, shape = 1)
N/A
Also known as the Fisk distribution.
distr6::Distribution -> distr6::SDistribution -> Loglogistic
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.
new()Creates a new instance of this R6 class.
Loglogistic$new(scale = NULL, shape = NULL, rate = NULL, decorators = NULL)
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.
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.
Loglogistic$mean(...)
...Unused.
mode()The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Loglogistic$mode(which = "all")
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
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).
Loglogistic$median()
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.
Loglogistic$variance(...)
...Unused.
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.
Loglogistic$skewness(...)
...Unused.
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.
Loglogistic$kurtosis(excess = TRUE, ...)
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
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.
Loglogistic$pgf(z, ...)
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
clone()The objects of this class are cloneable with this method.
Loglogistic$clone(deep = FALSE)
deepWhether to make a deep clone.
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 \(\alpha, \beta > 0\).
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
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