Triangle: The Triangle Distribution

Description

Density, distribution function, quantile function and random generation for the Triangle distribution with parameter theta.

Usage

dtriangle(x, theta, lower = 0, upper = 1, log = FALSE)
ptriangle(q, theta, lower = 0, upper = 1)
qtriangle(p, theta, lower = 0, upper = 1)
rtriangle(n, theta, lower = 0, upper = 1)

Arguments

x, q

vector of quantiles.

vector of probabilities.

number of observations. Must be a positive integer of length 1.

theta

the theta parameter which lies between lower and upper.

lower, upper

lower and upper limits of the distribution. Must be finite.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Value

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

Details

See triangle, the VGAM family function for estimating the parameter $\theta$ by maximum likelihood estimation.

Examples

Run this code

x = seq(-0.1, 1.1, by = 0.01); theta = 0.75
plot(x, dtriangle(x, theta = theta), type = "l", col = "blue", las = 1,
     main = "Blue is density, orange is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles",
     ylim = c(0,2), ylab = "")
abline(h = 0, col = "blue", lty = 2)
lines(x, ptriangle(x, theta = theta), col = "orange")
probs = seq(0.1, 0.9, by = 0.1)
Q = qtriangle(probs, theta = theta)
lines(Q, dtriangle(Q, theta = theta), col = "purple", lty = 3, type = "h")
ptriangle(Q, theta = theta) - probs    # Should be all zero
abline(h = probs, col = "purple", lty = 3)