triangle: The Triangle Distribution
In barryrowlingson/opVaR: Computes operational risk

Description Usage Arguments Details Value Author(s) References See Also Examples

These functions provide information about the triangle distribution on the interval from a to b with a maximum at c. dtriangle gives the density, ptriangle gives the distribution function, qtriangle gives the quantile function, and rtriangle generates n random deviates.

dtriangle(q, a=0, b=1, c=0.5)
ptriangle(q, a=0, b=1, c=0.5)
qtriangle(p, a=0, b=1, c=0.5)
rtriangle(n, a=0, b=1, c=0.5)

`q`	vector of quantiles.
`p`	vector of probabilities.
`a`	lower limit of the distribution.
`b`	upper limit of the distribution.
`c`	mode of the distribution.
`n`	number of observations. If `length(n) > 1`, the length is taken to be the number required.

All probabilities are lower tailed probabilties.

a, b, and c may be appropriate length vectors except in the case of rtriangle.

rtriangle is derived from a draw from runif.

The triangle distribution has density:

f(x) = 2(x-a) / [(b-a)(c-a)]

for a <= x < c.

f(x) = 2(b-x) / [(b-a)(b-c)]

for c <= x <= b. f(x) = 0 elsewhere.

The mean and variance are:

E(x) = (a + b + c) / 3

V(x) = (a^2 + b^2 + c^2 - ab - ac - bc) / 18

dtriangle gives the density, ptriangle gives the distribution function, qtriangle gives the quantile function, and rtraingle generates random deviates.

Invalid arguments will result in return value NaN or NA.

Rob Carnell

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth \& Brooks/Cole.

.Random.seed about random number generation, runif, etc for other distributions.

## view the distribution
tri <- rtriangle(100000, 1, 5, 3)
hist(tri, breaks=100, main="Triangle Distribution", xlab="x")

mean(tri) # 1/3*(1 + 5 + 3) = 3
var(tri)  # 1/18*(1^2 + 3^2 + 5^2 - 1*5 - 1*3 - 5*3) = 0.666667

dtriangle(0.5, 0, 1, 0.5) # 2/(b-a) = 2

qtriangle(ptriangle(0.7)) # 0.7