VGAM: triangleUC – R documentation

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triangleUC

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.

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

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 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) 
## End(Not run)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13