ING: Inverse Gamma distribution for fitting a GAMLSS

In gamlss.dist: Distributions to be used for GAMLSS modelling.

Description

The function ING() defines the Inverse Gamma distribution, a two parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(), with parameters mu (the mode) and sigma. The functions dING, pING, qING and rING define the density, distribution function, quantile function and random generation for the ING parameterization of the Inverse Gamma distribution.

Usage

ING(mu.link = "log", sigma.link="log")
dING(x, mu = 2, sigma = 1, log = FALSE)
pING(q, mu = 2, sigma = 1, lower.tail = TRUE, log.p = FALSE)
qING(p, mu = 2, sigma = 1, lower.tail = TRUE, log.p = FALSE, max.value = 1000)
rING(n, mu = 2, sigma = 1)

Arguments

mu.link	Defines the mu.link, with "log" link as the default for the mu parameter
sigma.link	Defines the sigma.link, with "log" as the default for the sigma parameter
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 length(n) > 1, the length is taken to be the number required
max.value	constant; generates a sequence of values for the cdf function

Details

The parameterization of the Inverse Gamma distribution in the function ING is

f(y|mu, sigma) = ([mu*(alpha+1)]^{alpha})/Gamma(alpha)*y^{(-(alpha+1))}*exp{-(mu*(alpha+1)}/y)

where alpha = 1/(sigma^2) for y>0, mu>0 and sigma>0.

Value

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

Note

For the function ING(), mu is the mode of the Inverse Gamma distribution.

Author(s)

Bob Rigby [e-mail], Mikis Stasinopoulos [e-mail], Fiona McElduff [e-mail] and Kalliope Akantziliotou

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.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.

See Also

gamlss.family

Examples

par(mfrow=c(2,2))
y<-seq(0.2,20,0.2)
plot(y, dING(y), type="l")
q <- seq(0.2, 20, 0.2)
plot(q, pING(q), type="l")
p<-seq(0.0001,0.999,0.05)
plot(p , qING(p), type="l")
dat <- rING(50)
hist(dat)
#summary(gamlss(dat~1, family="ING"))

gamlss.dist documentation built on May 2, 2019, 5:20 p.m.