Triangle {VGAM}R Documentation

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.

Details

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

Value

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

Author(s)

T. W. Yee

See Also

triangle.

Examples

## Not run: 
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)
## End(Not run)

[Package VGAM version 0.7-7 Index]