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

The function `GA`

defines the gamma distribution, a two parameter distribution, for a
`gamlss.family`

object to be used in GAMLSS fitting using the
function `gamlss()`

. The parameterization used has the mean of the distribution equal to *mu* and the variance equal to
*(sigma^2)*(mu^2)*.
The functions `dGA`

, `pGA`

, `qGA`

and `rGA`

define the density, distribution function, quantile function and random
generation for the specific parameterization of the gamma distribution defined by function `GA`

.

1 2 3 4 5 |

`mu.link` |
Defines the |

`sigma.link` |
Defines the |

`x,q` |
vector of quantiles |

`mu` |
vector of location parameter values |

`sigma` |
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 |

The specific parameterization of the gamma distribution used in `GA`

is

*f(y|mu,sigma)=(y^((1/sigma^2)-1)*exp[-y/((sigma^2)*mu)])/((sigma^2*mu)^(1/sigma^2) Gamma(1/sigma^2)) *

for *y>0*, *μ>0* and *σ>0*.

`GA()`

returns a `gamlss.family`

object which can be used to fit a gamma distribution in the `gamlss()`

function.
`dGA()`

gives the density, `pGA()`

gives the distribution
function, `qGA()`

gives the quantile function, and `rGA()`

generates random deviates. The latest functions are based on the equivalent `R`

functions for gamma distribution.

*mu* is the mean of the distribution in `GA`

. In the function `GA`

, *sigma* is the square root of the
usual dispersion parameter for a GLM gamma model. Hence *sigma*mu* is the standard deviation of the distribution defined in `GA`

.

Mikis Stasinopoulos [email protected], Bob Rigby and Calliope Akantziliotou

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.

1 2 3 4 5 6 7 8 | ```
GA()# gives information about the default links for the gamma distribution
# dat<-rgamma(100, shape=1, scale=10) # generates 100 random observations
# fit a gamlss model
# gamlss(dat~1,family=GA)
# fits a constant for each parameter mu and sigma of the gamma distribution
newdata<-rGA(1000,mu=1,sigma=1) # generates 1000 random observations
hist(newdata)
rm(dat,newdata)
``` |

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