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.

## 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 $$\gamma >= 0$$.

## Distribution support

The distribution is supported on the non-negative Reals.

## Default Parameterisation

ShiftLLogis(scale = 1, shape = 1, location = 0)

N/A

N/A

## References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

## 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.

alias

Alias of the distribution.

packages

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

## Active bindings

properties

Returns distribution properties, including skewness type and symmetry.

## Methods

Inherited methods

### Method new()

Creates a new instance of this R6 class.

...

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).

### 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.

#### 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

deep

Whether to make a deep clone.