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 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 \(\alpha, \beta > 0\).

The distribution is supported on the non-negative Reals.

LLogis(scale = 1, shape = 1)

N/A

Also known as the Fisk distribution.

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`

,
`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`

,
`Lognormal`

,
`Matdist`

,
`NegativeBinomial`

,
`Normal`

,
`Pareto`

,
`Poisson`

,
`Rayleigh`

,
`ShiftedLoglogistic`

,
`StudentTNoncentral`

,
`StudentT`

,
`Triangular`

,
`Uniform`

,
`Wald`

,
`Weibull`

,
`WeightedDiscrete`

`distr6::Distribution`

-> `distr6::SDistribution`

-> `Loglogistic`

`name`

Full name of distribution.

`short_name`

Short name of distribution for printing.

`description`

Brief description of the distribution.

`alias`

Alias of the distribution.

`packages`

Packages required to be installed in order to construct the distribution.

`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()`

`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.

`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).

`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)`

.

`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.

`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.

`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.

`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.