triangular {mc2d}

The Triangular Distribution

Description

Density, distribution function, quantile function and random generation for the triangular distribution with minimum equal to ‘⁠min⁠’, mode equal ‘⁠mode⁠’ (alternatively, mean equal ‘⁠mean⁠’) and maximum equal to ‘⁠max⁠’.

Usage

dtriang(x, min = -1, mode = 0, max = 1, log = FALSE, mean = 0)

ptriang(
  q,
  min = -1,
  mode = 0,
  max = 1,
  lower.tail = TRUE,
  log.p = FALSE,
  mean = 0
)

qtriang(
  p,
  min = -1,
  mode = 0,
  max = 1,
  lower.tail = TRUE,
  log.p = FALSE,
  mean = 0
)

rtriang(n, min = -1, mode = 0, max = 1, mean = 0)

Arguments

x, q

vector of quantiles.

min

vector of minima.

mode

vector of modes.

max

vector of maxima.

log, log.p

logical; if ‘⁠TRUE⁠’, probabilities ‘⁠p⁠’ are given as ‘⁠log(p)⁠’.

mean

Vector of means, can be specified in place of ‘⁠mode⁠’ as an alternative parametrization.

lower.tail

logical; if ‘⁠TRUE⁠’ (default), probabilities are ‘⁠P[X <= x]⁠’, otherwise, ‘⁠P[X > x]⁠’.

p

vector of probabilities.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

If ‘⁠min == mode == max⁠’, there is no density in that case and ‘⁠dtriang⁠’ will return ‘⁠NaN⁠’ (the error condition) (Similarity with Uniform).

‘⁠mode⁠’ or ‘⁠mean⁠’ can be specified, but not both. Note: ‘⁠mean⁠’ is the last parameter for back-compatibility. A warning will be provided if some combinations of ‘⁠min⁠’, ‘⁠mean⁠’ and ‘⁠max⁠’ leads to impossible mode.

Value

‘⁠dtriang⁠’ gives the density, ‘⁠ptriang⁠’ gives the distribution function, ‘⁠qtriang⁠’ gives the quantile function, and ‘⁠rtriang⁠’ generates random deviates.

Examples

curve(dtriang(x, min=3, mode=6, max=10), from = 2, to = 11, ylab="density")
## Alternative parametrization
curve(dtriang(x, min=3, mean=6, max=10), from = 2, to = 11, add=TRUE, lty=2)
##no density when  min == mode == max
dtriang(c(1,2,3),min=2,mode=2,max=2)