JSUo {gamlss.dist} | R Documentation |
The original Johnson's Su distribution for fitting a GAMLSS
Description
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.
Usage
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)
Arguments
mu.link |
Defines the |
sigma.link |
Defines the |
nu.link |
Defines the |
tau.link |
Defines the |
x , q |
vector of quantiles |
mu |
vector of location parameter values |
sigma |
vector of scale parameter values |
nu |
vector of skewness |
tau |
vector of kurtosis |
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 |
Details
The probability density function of the orininal Jonhson's SU distribution, (JSUo
), is defined as
for ,
,
,
and
.
where
,
, see pp. 389-390 of Rigby et al. (2019).
Value
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.
Warning
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)
Author(s)
Mikis Stasinopoulos and Bob Rigby
References
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.
Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://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, doi:10.18637/jss.v023.i07.
Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC. doi:10.1201/b21973
(see also https://www.gamlss.com/).
See Also
Examples
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)