R: Skew-Normal Distribution

skewnorm {VGAM} | R Documentation

## Skew-Normal Distribution

### Description

Density and random generation for the univariate skew-normal distribution.

### Usage

    dskewnorm(x, location = 0, scale = 1, shape = 0, log = FALSE)
    rskewnorm(n, location = 0, scale = 1, shape = 0)

### Arguments

`x` | vector of quantiles.

`n` | number of observations. Same as `runif`.
`location` | The location parameter xi. A vector.
`scale` | The scale parameter w. A positive vector.
`shape` | The shape parameter. It is called alpha in `skewnormal`.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### Details

See `skewnormal`, which currently only estimates the shape parameter. More generally here, Z = xi + w * Y where Y has a standard skew-normal distribution (see `skewnormal`), xi is the location parameter and w is the scale parameter.

### Value

`dskewnorm` gives the density, `rskewnorm` generates random deviates.

### Note

The default values of all three parameters corresponds to the skew-normal being the standard normal distribution.

### Author(s)

T. W. Yee

### References

`http://tango.stat.unipd.it/SN`.

### See Also

`skewnormal`.

### Examples

    ## Not run:  N <- 200  # Grid resolution
    shape <- 7; x <- seq(-4, 4, len = N)
    plot(x, dskewnorm(x, shape = shape), type = "l", col = "blue", las = 1,
         ylab = "", lty = 1, lwd = 2)
    abline(v = 0, h = 0, col = "grey")
    lines(x, dnorm(x), col = "orange", lty = 2, lwd = 2)
    legend("topleft", leg = c(paste("Blue = dskewnorm(x, ", shape,")", sep = ""),
           "Orange = standard normal density"), lty = 1:2, lwd = 2,
           col = c("blue", "orange"))
    ## End(Not run)

[Package VGAM version 1.1-3 Index]