IG {gamlss.dist} | R Documentation |
The function IG()
, or equivalently Inverse.Gaussian()
, defines the inverse Gaussian distribution,
a two parameter distribution, for a gamlss.family
object to be used in GAMLSS fitting
using the function gamlss()
.
The functions dIG
, pIG
, qIG
and rIG
define the density, distribution function, quantile function and random
generation for the specific parameterization of the Inverse Gaussian distribution defined by function IG
.
IG(mu.link = "log", sigma.link = "log") dIG(x, mu = 1, sigma = 1, log = FALSE) pIG(q, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE) qIG(p, mu = 1, sigma = 1, lower.tail = TRUE, log.p = FALSE) rIG(n, mu = 1, sigma = 1, ...)
mu.link |
Defines the mu.link , with "log" link as the default for the mu parameter |
sigma.link |
Defines the sigma.link , with "log" link 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 |
... |
... can be used to pass the uppr.limit argument to qIG |
Definition file for inverse Gaussian distribution.
f(y|mu,sigma)=(1/(sqrt(2*pi*sigma^2*y^3))* exp(-(y-mu)^2/(2*mu^2*sigma^2*y))
for y>0, μ>0 and σ>0.
returns a gamlss.family
object which can be used to fit a inverse Gaussian distribution in the gamlss()
function.
mu is the mean and (sigma^2)*(mu^3) is the variance of the inverse Gaussian
Mikis Stasinopoulos, 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.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.
gamlss.family
, GA
, GIG
IG()# gives information about the default links for the normal distribution # library(gamlss) # data(rent) # gamlss(R~cs(Fl),family=IG, data=rent) # plot(function(x)dIG(x, mu=1,sigma=.5), 0.01, 6, main = "{Inverse Gaussian density mu=1,sigma=0.5}") plot(function(x)pIG(x, mu=1,sigma=.5), 0.01, 6, main = "{Inverse Gaussian cdf mu=1,sigma=0.5}")