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, 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

### 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 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)

[Package VGAM version 1.1-1 Index]