NET {gamlss.dist} | R Documentation |
This function defines the Power Exponential t distribution (NET), a four parameter distribution, for a gamlss.family
object to be used for a
GAMLSS fitting using the function gamlss()
. The functions dNET
,
pNET
define the density and distribution function the NET distribution.
NET(mu.link = "identity", sigma.link = "log") pNET(q, mu = 5, sigma = 0.1, nu = 1, tau = 2) dNET(x, mu = 0, sigma = 1, nu = 1.5, tau = 2, log = FALSE)
mu.link |
Defines the mu.link , with "identity" link as the default for the mu parameter. Other links are "inverse", "log" and "own" |
sigma.link |
Defines the sigma.link , with "log" link as the default for the sigma parameter. Other links are "inverse", "identity" and "own" |
x,q |
vector of quantiles |
mu |
vector of location parameter values |
sigma |
vector of scale parameter values |
nu |
vector of nu parameter values |
tau |
vector of tau parameter values |
log |
logical; if TRUE, probabilities p are given as log(p). |
The NET distribution was introduced by Rigby and Stasinopoulos (1994) as a robust distribution for a response
variable with heavier tails than the normal. The NET
distribution is the abbreviation of the Normal Exponential Student t distribution.
The NET distribution is a four parameter continuous distribution, although in the GAMLSS implementation only
the two parameters, mu
and sigma
, of the distribution are modelled with
nu
and tau
fixed.
The distribution takes its names because it is normal up to
nu
, Exponential from nu
to tau
(hence abs(nu)<=abs(tau)
) and Student-t with
nu*tau-1
degrees of freedom after tau
. Maximum
likelihood estimator of the third and forth parameter can be
obtained, using the GAMLSS functions, find.hyper
or prof.dev
.
NET()
returns a gamlss.family
object which can be used to fit a Box Cox Power Exponential distribution in the gamlss()
function.
dNET()
gives the density, pNET()
gives the distribution
function.
Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou
Rigby, R. A. and Stasinopoulos, D. M. (1994), Robust fitting of an additive model for variance heterogeneity, COMPSTAT : Proceedings in Computational Statistics, editors:R. Dutter and W. Grossmann, pp 263-268, Physica, Heidelberg.
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.
NET() # data(abdom) plot(function(x)dNET(x, mu=0,sigma=1,nu=2, tau=3), -5, 5) plot(function(x)pNET(x, mu=0,sigma=1,nu=2, tau=3), -5, 5) # fit NET with nu=1 and tau=3 # library(gamlss) #h<-gamlss(y~cs(x,df=3), sigma.formula=~cs(x,1), family=NET, # data=abdom, nu.start=2, tau.start=3) #plot(h)