Description Usage Arguments Details Value Author(s) References See Also Examples

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.

1 2 3 4 5 6 7 8 | ```
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)
``` |

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`nu.link` |
Defines the |

`tau.link` |
Defines the |

`x,q` |
vector of quantiles |

`mu` |
vector of location parameter values |

`sigma` |
vector of scale parameter values |

`nu` |
vector of skewness |

`tau` |
vector of kurtosis |

`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 |

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).

`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.

Bob Rigby and Mikis Stasinopoulos

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.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in http://www.gamlss.com/.

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.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
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")
``` |

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