gamlss.dist (version 5.0-0)

GE: Geometric distribution for fitting a GAMLSS

Description

The function GE() defines the Yule distribution, a one parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(), with mean equal to the parameter mu. The functions dGE, pGE, qGE and rGE define the density, distribution function, quantile function and random generation for the GE parameterization of the Geometric distribution.

Usage

GE(mu.link = "log")
dGE(x, mu = 2, log = FALSE)
pGE(q, mu = 2, lower.tail = TRUE, log.p = FALSE)
qGE(p, mu = 2, lower.tail = TRUE, log.p = FALSE, max.value=10000)
rGE(n, mu = 2)

Arguments

mu.link

Defines the mu.link, with "log" link as the default for the mu parameter

x, q

vector of quantiles

mu

vector of location 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

max.value

constant; generates a sequence of values for the cdf function

Value

returns a gamlss.family object which can be used to fit a Geometric distribution in the gamlss() function.

Details

The parameterization of the Geometric distribution in the function GE is $$f(y|mu) = (1-p)^y p$$ where \(p = 1/(mu+1)\) for \(y>=0\) and \(mu>0\).

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.

See Also

gamlss.family

Examples

par(mfrow=c(2,2))
y<-seq(0,20,1)
plot(y, dGE(y), type="h")
q <- seq(0, 20, 1)
plot(q, pGE(q), type="h")
p<-seq(0.0001,0.999,0.05)
plot(p , qGE(p), type="s")
dat <- rGE(100)
hist(dat)
#summary(gamlss(dat~1, family="GE"))