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.

Examples

Run this code

# 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)

# }

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