Exponential: Exponential Distribution Class

Description

Mathematical and statistical functions for the Exponential distribution, which is commonly used to model inter-arrival times in a Poisson process and has the memoryless property.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Exponential$new(rate = NULL, scale = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`rate`	numeric	arrival rate.
`scale`	numeric	scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Exponential distribution is parameterised with rate or scale as positive numerics. These are related via, $s c a l e = 1 / r a t e$ If scale is given then rate 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 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 Exponential distribution parameterised with rate, $λ$ , is defined by the pdf, $f (x) = λ e x p (- x λ)$ for $λ > 0$ .

The distribution is supported on the Positive Reals.

References

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

Examples

Run this code

# NOT RUN {
Exponential$new(rate = 4)
Exponential$new(scale = 3)

x = Exponential$new(verbose = TRUE) # Default is rate = 1

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

# }

Run the code above in your browser using DataLab

Last chance! 50% off unlimited learning