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.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Loglogistic$new(scale = 1, shape = 1, location = 0, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`shape`	numeric	shape parameter.
`scale`	numeric	scale parameter.
`location`	numeric	location parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Log-Logistic distribution is parameterised with shape and scale as positive numerics and location as a numeric.

Public Variables

Variable	Return
`name`	Name of distribution.
`short_name`	Id of distribution.
`description`	Brief description of distribution.

Public Methods

Accessor Methods	Link
`decorators()`	`decorators`
`traits()`	`traits`
`valueSupport()`	`valueSupport`
`variateForm()`	`variateForm`
`type()`	`type`
`properties()`	`properties`
`support()`	`support`
`symmetry()`	`symmetry`
`sup()`	`sup`
`inf()`	`inf`
`dmax()`	`dmax`
`dmin()`	`dmin`
`skewnessType()`	`skewnessType`
`kurtosisType()`	`kurtosisType`



Statistical Methods	Link
`pdf(x1, ..., log = FALSE, simplify = TRUE)`	`pdf`
`cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`cdf`
`quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE)`	`quantile.Distribution`
`rand(n, simplify = TRUE)`	`rand`
`mean()`	`mean.Distribution`
`variance()`	`variance`
`stdev()`	`stdev`
`prec()`	`prec`
`cor()`	`cor`
`skewness()`	`skewness`
`kurtosis(excess = TRUE)`	`kurtosis`
`entropy(base = 2)`	`entropy`
`mgf(t)`	`mgf`
`cf(t)`	`cf`
`pgf(z)`	`pgf`
`median()`	`median.Distribution`
`iqr()`	`iqr`
`mode(which = "all")`	`mode`



Parameter Methods	Link
`parameters(id)`	`parameters`
`getParameterValue(id, error = "warn")`	`getParameterValue`
`setParameterValue(..., lst = NULL, error = "warn")`	`setParameterValue`



Validation Methods	Link
`liesInSupport(x, all = TRUE, bound = FALSE)`	`liesInSupport`
`liesInType(x, all = TRUE, bound = FALSE)`	`liesInType`



Representation Methods	Link
`strprint(n = 2)`	`strprint`
`print(n = 2)`	`print`
`summary(full = T)`	`summary.Distribution`

Details

The 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 $\gamma >= 0$.

The distribution is supported on the non-negative Reals.

entropy, mgf and cf are omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

Also known as the Fisk distribution.

References

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

Examples

Run this code

# NOT RUN {
x <- Loglogistic$new(shape = 2, scale = 3)

# Update parameters
x$setParameterValue(scale = 2)
x$parameters()

# d/p/q/r
x$pdf(5:6)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }

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