skewunit (version 1.0)

triang: The triangular distribution

Description

Density, distribution function and random generation for the triangular distribution.

Usage

dtriang(x, log=FALSE)
ptriang(q, lower.tail=TRUE, log.p=FALSE)
rtriang(n)

Value

dtriang gives the density, ptriang gives the distribution function, and rtriang generates random deviates. The length of the result is determined by n for rasin, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

Arguments

x, q

vector of quantiles.

n

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

log, log.p

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

lower.tail

logical; if TRUE (default), probabilities are \(P[X\leq x]\), otherwise, \(P[X>x]\).

Author

Diego Gallardo

Details

The triangular distribution has density $$ f(x) = \left\{ \begin{array}{lr} 4x, & 0\leq x\leq 1/2,\\ 4(1-x), & 1/2<x\leq 1, \end{array} \right. $$ and cumulative distribution function $$ F(x) = \left\{ \begin{array}{lr} 2x^2, & 0\leq x\leq 1/2,\\ 2x^2-(2x-1)^2, & 1/2<x\leq 1, \end{array} \right. $$

Examples

dtriang(0.5)
ptriang(0.5)
rtriang(5)