R: Skew Normal Type 1 distribution for fitting a GAMLSS

SN1 {gamlss.dist} | R Documentation

## Skew Normal Type 1 distribution for fitting a GAMLSS

### Description

The function `SN1()` defines the Skew Normal Type 1 distribution, a three parameter distribution, for a `gamlss.family` object to be used in GAMLSS fitting using the function `gamlss()`, with parameters `mu`, `sigma` and `nu`. The functions `dSN1`, `pSN1`, `qSN1` and `rSN1` define the density, distribution function, quantile function and random generation for the `SN1` parameterization of the Skew Normal Type 1 distribution.

### Usage

    SN1(mu.link = "identity", sigma.link = "log", nu.link="identity")
    dSN1(x, mu = 0, sigma = 1, nu = 0, log = FALSE)
    pSN1(q, mu = 0, sigma = 1, nu = 0, lower.tail = TRUE, log.p = FALSE)
    qSN1(p, mu = 0, sigma = 1, nu = 0, lower.tail = TRUE, log.p = FALSE)
    rSN1(n, mu = 0, sigma = 1, nu = 0)

### Arguments

`mu.link` | Defines the `mu.link`, with "‘identity"’ links the default for the mu parameter
`sigma.link` | Defines the `sigma.link`, with "‘log"’ as the default for the sigma parameter
`nu.link` | Defines the `nu.link`, with "‘identity"’ as the default for the sigma parameter
`x, q` | vector of quantiles
`mu` | vector of location parameter values
`sigma` | vector of scale parameter values
`nu` | vector of scale parameter values
`log, log.p` | logical; if TRUE, probabilities p are given as log(p)
`lower.tail` | logical; if TRUE (default), probabilities are P[X <= x], otherwise P[X > x]
`p` | vector of probabilities
`n` | number of observations. If `length(n) > 1`, the length is taken to be the number required

### Details

The parameterization of the Skew Normal Type 1 distribution in the function `SN1` is ...

### Value

returns a gamlss.family object which can be used to fit a Skew Normal Type 1 distribution in the `gamlss()` function.

### Note

This is a special case of the Skew Exponential Power type 1 distribution (`SEP1`)where `tau=2`.

### Author(s)

Mikis Stasinopoulos, Bob Rigby and Fiona McElduff

### References

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, http://www.jstatsoft.org/v23/i07.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

### See Also

`gamlss.family`

### Examples

    par(mfrow=c(2,2))
    y<-seq(-3,3,0.2)
    plot(y, dSN1(y), type="l" , lwd=2)
    q<-seq(-3,3,0.2)
    plot(q, pSN1(q), ylim=c(0,1), type="l", lwd=2)
    p<-seq(0.0001,0.999,0.05)
    plot(p, qSN1(p), type="l", lwd=2)
    dat <- rSN1(100)
    hist(rSN1(100), nclass=30)

[Package gamlss.dist version 5.0-2 Index]