Logistic: Logistic Distribution Class

Description

Mathematical and statistical functions for the Logistic distribution, which is commonly used in logistic regression and feedforward neural networks.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Logistic$new(mean = 0, scale = 1, sd = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`mean`	numeric	location parameter.
`scale`	numeric	scale parameter.
`sd`	numeric	standard deviation, alternate scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Logistic distribution is parameterised with mean as a numeric and either scale or sd as positive numerics. These are related via, $$sd = scale*\pi/\sqrt(3)$$ If sd is given then scale is ignored.

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`



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 Logistic distribution parameterised with mean, $\mu$, and scale, $s$, is defined by the pdf, $$f(x) = exp(-(x-\mu)/s) / (s(1+exp(-(x-\mu)/s))^2)$$ for $\mu \epsilon R$ and $s > 0$.

The distribution is supported on the Reals.

References

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

Examples

Run this code

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

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(sd = 2)
x$parameters()

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

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

summary(x)

# }

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