# triangleUC: The Triangle Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```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

`triangle`, `topple`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ```## 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) ```