GIG {gamlss.dist}R Documentation

Generalized Inverse Gaussian distribution for fitting a GAMLSS

Description

The function GIG defines the generalized inverse gaussian distribution, a three parameter distribution, for a gamlss.family object to be used in GAMLSS fitting using the function gamlss(). The functions dGIG, pGIG, qGIG and rGIG define the density, distribution function, quantile function and random generation for the specific parameterization of the generalized inverse gaussian distribution defined by function GIG.

Usage

GIG(mu.link = "log", sigma.link = "log", 
                       nu.link = "identity")
dGIG(y, mu=1, sigma=1, nu=1,  
                      log = FALSE)
pGIG(q, mu=1, sigma=1, nu=1,  lower.tail = TRUE, 
                     log.p = FALSE)
qGIG(p, mu=1, sigma=1, nu=1,  lower.tail = TRUE, 
                     log.p = FALSE,lower.limit = 0,
                upper.limit = mu+10*sqrt(sigma^2*mu^3))
rGIG(n, mu=1, sigma=1, nu=1, ...)

Arguments

mu.link Defines the mu.link, with "log" link as the default for the mu parameter, other links are "inverse" and "identity"
sigma.link Defines the sigma.link, with "log" link as the default for the sigma parameter, other links are "inverse" and "identity"
nu.link Defines the nu.link, with "identity" link as the default for the nu parameter, other links are "inverse" and "log"
y,q vector of quantiles
mu vector of location parameter values
sigma vector of scale parameter values
nu vector of shape 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
lower.limit a constant, set to the value of 0 for the algorithm to know from where to begin looking for q
upper.limit a constant, set to the value of mu+10*sqrt(sigma\^2*mu\^3) for how far the algorithm should look for q
... for extra arguments

Details

The specific parameterization of the generalized inverse gaussian distribution used in GIG is f(y|mu,sigma,nu)=((c/mu)^nu)*(y^(nu-1))/(2*besselK(1/sigma,nu))*exp(-1/(2*sigma)*(c*y/mu+mu/(c*y))) where c = besselK(1/sigma,nu+1)/besselK(1/sigma,nu), for y>0, mu>0, sigma>0 and -Inf>nu>Inf.

Value

GIG() returns a gamlss.family object which can be used to fit a generalized inverse gaussian distribution in the gamlss() function. dGIG() gives the density, pGIG() gives the distribution function, qGIG() gives the quantile function, and rGIG() generates random deviates.

Note

Author(s)

Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk, Bob Rigby r.rigby@londonmet.ac.uk and Nicoleta Motpan

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.londonmet.ac.uk/gamlss/).

Jorgensen B. (1982) Statistical properties of the generalized inverse Gaussian distribution, Series: Lecture notes in statistics; 9, New York : Springer-Verlag.

See Also

gamlss, gamlss.family, GI

Examples

y<-rGIG(100,mu=1,sigma=1, nu=-0.5) # generates 1000 random observations 
histDist(y, family=GIG) 

[Package gamlss.dist version 1.6-0 Index]