R: The exponential generalized Beta type 2 distribution for...

EGB2 {gamlss.dist} | R Documentation

## The exponential generalized Beta type 2 distribution for fitting a GAMLSS

### Description

This function defines the generalized t distribution, a four parameter distribution. The response variable is in the range from minus infinity to plus infinity. The functions `dEGB2`, `pEGB2`, `qEGB2` and `rEGB2` define the density, distribution function, quantile function and random generation for the generalized beta type 2 distribution.

### Usage

    EGB2(mu.link = "identity", sigma.link = "log", nu.link = "log",
          tau.link = "log")
    dEGB2(x, mu = 0, sigma = 1, nu = 1, tau = 0.5, log = FALSE)
    pEGB2(q, mu = 0, sigma = 1, nu = 1, tau = 0.5, lower.tail = TRUE,
          log.p = FALSE)
    qEGB2(p, mu = 0, sigma = 1, nu = 1, tau = 0.5, lower.tail = TRUE,
          log.p = FALSE)
    rEGB2(n, mu = 0, sigma = 1, nu = 1, tau = 0.5)

### Arguments

`mu.link` | Defines the `mu.link`, with "identity" link as the default for the `mu` parameter.
`sigma.link` | Defines the `sigma.link`, with "log" link as the default for the `sigma` parameter.
`nu.link` | Defines the `nu.link`, with "log" link as the default for the `nu` parameter.
`tau.link` | Defines the `tau.link`, with "log" link as the default for the `tau` parameter.
`x,q` | vector of quantiles
`mu` | vector of location parameter values
`sigma` | vector of scale parameter values
`nu` | vector of skewness `nu` parameter values
`tau` | vector of kurtosis `tau` 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 probability density function of the Generalized Beta type 2, (`GB2`), is defined as

f(y|mu,sigma,nu,tau)=exp{nu*z}(abs(sigma)*Beta(nu.tau)*(1+exp(z))^(nu+tau) )^(-1)

for -Inf<y<Inf, where z=(y-mu)/sigma and -Inf<mu<Inf, -Inf<sigma<Inf, nu>0 and tau>0, McDonald and Xu (1995).

### Value

`EGB2()` returns a `gamlss.family` object which can be used to fit the EGB2 distribution in the `gamlss()` function. `dEGB2()` gives the density, `pEGB2()` gives the distribution function, `qEGB2()` gives the quantile function, and `rEGB2()` generates random deviates.

### Author(s)

Bob Rigby and Mikis Stasinopoulos mikis.stasinopoulos@gamlss.org

### 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`, `JSU`, `BCT`

### Examples

    EGB2()   #
    y<- rEGB2(200, mu=5, sigma=2, nu=1, tau=4)
    library(MASS)
    truehist(y)
    fx<-dEGB2(seq(min(y), 20, length=200), mu=5 ,sigma=2, nu=1, tau=4)
    lines(seq(min(y),20,length=200),fx)
    # something funny here
    # library(gamlss)
    # histDist(y, family=EGB2, n.cyc=60)
    integrate(function(x) x*dEGB2(x=x, mu=5, sigma=2, nu=1, tau=4), -Inf, Inf)
    curve(dEGB2(x, mu=5 ,sigma=2, nu=1, tau=4), -10, 10, main = "The EGB2  density
                 mu=5, sigma=2, nu=1, tau=4")

[Package gamlss.dist version 5.0-2 Index]