# triangular: The Triangular Distribution In mc2d: Tools for Two-Dimensional Monte-Carlo Simulations

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```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

 ```1 2 3 4 5``` ```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) ```

mc2d documentation built on July 5, 2021, 5:09 p.m.