Triangle {VGAM}R Documentation

The Triangle Distribution


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


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)


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.


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


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


T. W. Yee

See Also



## 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]