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)
    qtriangle(p, theta, lower=0, upper=1)
    rtriangle(n, theta, lower=0, upper=1)

### Arguments

`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.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### 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

### See Also

`triangle`.

### 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, 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 0.7-9 Index]