triangular function

The Triangular Distribution

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 .

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.

Returns

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

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.

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)