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)
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.

### 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

`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 0.7-7 Index]