SN2 {gamlss.dist} | R Documentation |
Skew Normal Type 2 distribution for fitting a GAMLSS
Description
The function SN2()
defines the Skew Normal Type 2 distribution, a three parameter distribution, for a gamlss.family
object to be used in GAMLSS fitting using the function gamlss()
, with parameters mu
, sigma
and nu
. The functions dSN2
, pSN2
, qSN2
and rSN2
define the density, distribution function, quantile function and random generation for the SN2
parameterization of the Skew Normal Type 2 distribution.
Usage
SN2(mu.link = "identity", sigma.link = "log", nu.link = "log")
dSN2(x, mu = 0, sigma = 1, nu = 2, log = FALSE)
pSN2(q, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
qSN2(p, mu = 0, sigma = 1, nu = 2, lower.tail = TRUE, log.p = FALSE)
rSN2(n, mu = 0, sigma = 1, nu = 2)
Arguments
mu.link |
Defines the |
sigma.link |
Defines the |
nu.link |
Defines the |
x , q |
vector of quantiles |
mu |
vector of location parameter values |
sigma |
vector of scale parameter values |
nu |
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 |
Details
The parameterization of the Skew Normal Type 2 distribution in the function SN2
is
if
if
for ,
,
and
where
and
see pp. 380-381 of Rigby et al. (2019).
Value
returns a gamlss.family object which can be used to fit a Skew Normal Type 2 distribution in the gamlss()
function.
Note
This is a special case of the Skew Exponential Power type 3 distribution (SEP3
)where tau=2
.
Author(s)
Mikis Stasinopoulos, Bob Rigby and Fiona McElduff.
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.
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
par(mfrow=c(2,2))
y<-seq(-3,3,0.2)
plot(y, dSN2(y), type="l" , lwd=2)
q<-seq(-3,3,0.2)
plot(q, pSN2(q), ylim=c(0,1), type="l", lwd=2)
p<-seq(0.0001,0.999,0.05)
plot(p, qSN2(p), type="l", lwd=2)
dat <- rSN2(100)
hist(rSN2(100), nclass=30)