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 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
.
GA(mu.link = "log", sigma.link ="log")
dGA(x, mu = 1, sigma = 1, log = FALSE)
pGA(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qGA(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE)
rGA(n, mu = 1, sigma = 1)
Defines the mu.link
, with "log" link as the default for the mu parameter, other links are "inverse", "identity" ans "own"
Defines the sigma.link
, with "log" link as the default for the sigma parameter, other link is the "inverse", "identity" and "own"
vector of quantiles
vector of location parameter values
vector of scale parameter values
logical; if TRUE, probabilities p are given as log(p).
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]
vector of probabilities.
number of observations. If length(n) > 1
, the length is
taken to be the number required
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.
The specific parameterization of the gamma distribution used in GA
is
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.
# NOT RUN {
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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