Tikuv {VGAM} | R Documentation

## A Short-tailed Symmetric Distribution

### Description

Density, cumulative distribution function, quantile function and random generation for the short-tailed symmetric distribution of Tiku and Vaughan (1999).

### Usage

    dtikuv(x, d, mean=0, sigma=1, log=FALSE)
    ptikuv(q, d, mean=0, sigma=1)
    qtikuv(p, d, mean=0, sigma=1, ...)
    rtikuv(n, d, mean=0, sigma=1, Smallno=1.0e-6)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Must be a positive integer of length 1.
`d, mean, sigma` | arguments for the parameters of the distribution. See `tikuv` for more details. For `rtikuv`, arguments `mean` and `sigma` must be of length 1.
`Smallno` | Numeric, a small value used by the rejection method for determining the lower and upper limits of the distribution. That is, `ptikuv(L) < Smallno` and `ptikuv(U) > 1-Smallno` where `L` and `U` are the lower and upper limits respectively.
`...` | Arguments that can be passed into `uniroot`.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### Details

See `tikuv` for more details.

### Value

`dtikuv` gives the density, `ptikuv` gives the cumulative distribution function, `qtikuv` gives the quantile function, and `rtikuv` generates random deviates.

### Author(s)

T. W. Yee

### See Also

`tikuv`.

### Examples

    ## Not run:
    x = seq(-5, 5, len=401)
    plot(x, dnorm(x), type="l", col="black", ylab="",
         main="Black is standard normal, others are dtikuv(x, d)")
    lines(x, dtikuv(x, d=-10), col="red")
    lines(x, dtikuv(x, d=-1 ), col="blue")
    lines(x, dtikuv(x, d= 1 ), col="green")
    legend(2, 0.35, col=c("red","blue","green"), lty=rep(1, len=3),
           legend=paste("d =", c(-10, -1, 1)))

    plot(x, pnorm(x), type="l", col="black", ylab="",
         main="Black is standard normal, others are ptikuv(x, d)")
    lines(x, ptikuv(x, d=-10), col="red")
    lines(x, ptikuv(x, d=-1 ), col="blue")
    lines(x, ptikuv(x, d= 1 ), col="green")
    legend(2, 0.35, col=c("red","blue","green"), lty=rep(1, len=3),
           legend=paste("d =", c(-10, -1, 1)))

    probs = seq(0.1, 0.9, by=0.1)
    ptikuv(qtikuv(p=probs, d= 1), d=1) - probs  # Should be all 0
    ## End(Not run)

[Package VGAM version 0.7-9 Index]