VGAM (version 0.7-7)

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)
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.

p

vector of probabilities.

n

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.

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.

See Also

triangle.

Examples

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, red 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="red")
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)