triangleUC: The Triangle Distribution

In VGAMdata: Data Supporting the 'VGAM' Package

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, lower.tail = TRUE, log.p = FALSE)
qtriangle(p, theta, lower = 0, upper = 1, lower.tail = TRUE, log.p = FALSE)
rtriangle(n, theta, lower = 0, upper = 1)

Arguments

x, q	vector of quantiles.
p	vector of probabilities.
n	number of observations. Same as runif.
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.
lower.tail, log.p	Same meaning as in pnorm or qnorm.

Details

See triangle, the VGAM family function for estimating the parameter \theta by maximum likelihood estimation, however the regular conditions do not hold so the algorithm crawls to the solution if lucky.

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 and Kai Huang

See Also

triangle, topple.

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, orange is the CDF",
     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) 
## End(Not run)

VGAMdata documentation built on Sept. 17, 2024, 9:09 a.m.