Rayleigh: Rayleigh Distribution Class

Description

Mathematical and statistical functions for the Rayleigh distribution, which is commonly used to model random complex numbers..

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Rayleigh$new(mode = 1, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`mode`	numeric	mode, scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Rayleigh distribution is parameterised with mode as a non-negative 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`



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`
`plot()`	Coming Soon.
`qqplot()`	Coming Soon.

Details

The Rayleigh distribution parameterised with mode (or scale), $\alpha$, is defined by the pdf, $$f(x) = x/\alpha^2 exp(-x^2/(2\alpha^2))$$ for $\alpha > 0$.

The distribution is supported on $[0, \infty)$.

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

References

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

Examples

Run this code

# NOT RUN {
x <- Rayleigh$new(mode = 2)

# Update parameters
x$setParameterValue(mode = 4)
x$parameters()

# d/p/q/r
x$pdf(1:4)
x$cdf(2)
x$quantile(0.42)
x$rand(4)

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

summary(x)

# }

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