distr6 (version 1.3.6)

Triangular: Triangular Distribution Class

Description

Mathematical and statistical functions for the Triangular distribution, which is commonly used to model population data where only the minimum, mode and maximum are known (or can be reliably estimated), also to model the sum of standard uniform distributions.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Triangular$new(lower = 0, upper = 1, mode = 0.5, symmetric = FALSE, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
lower	numeric	lower limit.
upper	numeric	upper limit.
mode	numeric	mode.
symmetric	logical	see details.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Triangular distribution is parameterised with lower, upper and mode as numerics. If symmetric = TRUE then the mode parameter is determined automatically and is defined by $$mode = (lower + upper) /2$$ this cannot be changed after construction. If symmetric = FALSE (default) then mode can be updated after construction.

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 Triangular distribution parameterised with lower limit, \(a\), upper limit, \(b\), and mode, \(c\), is defined by the pdf, \(f(x) = 0, x < a\) \(f(x) = 2(x-a)/((b-a)(c-a)), a \le x < c\) \(f(x) = 2/(b-a), x = c\) \(f(x) = 2(b-x)/((b-a)(b-c)), c < x \le b\) \(f(x) = 0, x > b\) for \(a,b,c \ \in \ R\), \(a \le c \le b\).

The distribution is supported on \([a, b]\).

References

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

See Also

listDistributions for all available distributions. Uniform for the Uniform distribution.

Examples

# NOT RUN {
Triangular$new(lower = 2, upper = 5, symmetric = TRUE)
Triangular$new(lower = 2, upper = 5, symmetric = FALSE) # Note mode defaults to a symmetric shape
Triangular$new(lower = 2, upper = 5, mode = 4)

# You can view the type of Triangular distribution with $description
Triangular$new(lower = 2, upper = 5, symmetric = TRUE)$description
Triangular$new(lower = 2, upper = 5, symmetric = FALSE)$description

x = Triangular$new(lower = -1, upper = 1)

# Update parameters
x$setParameterValue(lower = 2, upper = 7)
x$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)

# }