JSUo {gamlss.dist} | R Documentation |
This function defines the , a four parameter distribution, for a gamlss.family
object to be used for a
GAMLSS fitting using the function gamlss()
. The functions dJSUo
,
pJSUo
, qJSUo
and rJSUo
define the density, distribution function, quantile function and random
generation for the the Johnson's Su distribution.
JSUo(mu.link = "identity", sigma.link = "log", nu.link = "identity", tau.link = "log") dJSUo(x, mu = 0, sigma = 1, nu = 0, tau = 1, log = FALSE) pJSUo(q, mu = 0, sigma = 1, nu = 0, tau = 1, lower.tail = TRUE, log.p = FALSE) qJSUo(p, mu = 0, sigma = 1, nu = 0, tau = 1, lower.tail = TRUE, log.p = FALSE) rJSUo(n, mu = 0, sigma = 1, nu = 0, tau = 1)
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" |
nu.link |
Defines the nu.link , with "identity" link as the default for the nu parameter. Other links are "inverse", "log" ans "own" |
tau.link |
Defines the tau.link , with "log" link as the default for the tau 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 skewness nu parameter values |
tau |
vector of kurtosis tau 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 |
The probability density function of the orininal Jonhson's SU distribution, (JSU
), is defined as
f(y|mu,sigma,nu,tau)=tau/(sigma)*(1/(z^2+1)^.5)*(1/2*Pi)^(.5)exp(-.5r^2)
for 0<y<0, mu=(-Inf,+Inf), sigma>0, nu=(-Inf,+Inf) and tau>0. where z=(y-mu)/sigma, nu + tau* asinh(z).
JSUo()
returns a gamlss.family
object which can be used to fit a Johnson's Su distribution in the gamlss()
function.
dJSUo()
gives the density, pJSUo()
gives the distribution
function, qJSUo()
gives the quantile function, and rJSUo()
generates random deviates.
The function JSU
uses first derivatives square in the fitting procedure so
standard errors should be interpreted with caution. It is recomented to be used only with method=mixed(2,20)
Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk and Bob Rigby r.rigby@londonmet.ac.uk
Johnson, N. L. (1954). Systems of frequency curves derived from the first law of Laplace., Trabajos de Estadistica, 5, 283-291.
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.
JSU() plot(function(x)dJSUo(x, mu=0,sigma=1,nu=-1, tau=.5), -4, 15, main = "The JSUo density mu=0,sigma=1,nu=-1, tau=.5") plot(function(x) pJSUo(x, mu=0,sigma=1,nu=-1, tau=.5), -4, 15, main = "The JSUo cdf mu=0, sigma=1, nu=-1, tau=.5") # library(gamlss) # data(abdom) # h<-gamlss(y~cs(x,df=3), sigma.formula=~cs(x,1), family=JSUo, # data=abdom, method=mixed(2,20)) # plot(h)