dSEP1
, dSEP2
, dSEP3
and dSEP4
define the probability distribution functions,
the functions pSEP1
, pSEP2
, pSEP3
and pSEP4
define the cumulative distribution functions
the functions qSEP1
, qSEP2
, qSEP3
and qSEP4
define the inverse cumulative distribution functions and
the functions rSEP1
, rSEP2
, rSEP3
and rSEP4
define the random generation for the Skew exponential power
distributions.SEP1(mu.link = "identity", sigma.link = "log", nu.link = "identity",
tau.link = "log")
dSEP1(x, mu = 0, sigma = 1, nu = 0, tau = 2, log = FALSE)
pSEP1(q, mu = 0, sigma = 1, nu = 0, tau = 2, lower.tail = TRUE,
log.p = FALSE)
qSEP1(p, mu = 0, sigma = 1, nu = 0, tau = 2, lower.tail = TRUE,
log.p = FALSE)
rSEP1(n, mu = 0, sigma = 1, nu = 0, tau = 2)SEP2(mu.link = "identity", sigma.link = "log", nu.link = "identity",
tau.link = "log")
dSEP2(x, mu = 0, sigma = 1, nu = 0, tau = 2, log = FALSE)
pSEP2(q, mu = 0, sigma = 1, nu = 0, tau = 2, lower.tail = TRUE,
log.p = FALSE)
qSEP2(p, mu = 0, sigma = 1, nu = 0, tau = 2, lower.tail = TRUE,
log.p = FALSE)
rSEP2(n, mu = 0, sigma = 1, nu = 0, tau = 2)
SEP3(mu.link = "identity", sigma.link = "log", nu.link = "log",
tau.link = "log")
dSEP3(x, mu = 0, sigma = 1, nu = 2, tau = 2, log = FALSE)
pSEP3(q, mu = 0, sigma = 1, nu = 2, tau = 2, lower.tail = TRUE,
log.p = FALSE)
qSEP3(p, mu = 0, sigma = 1, nu = 2, tau = 2, lower.tail = TRUE,
log.p = FALSE)
SEP4(mu.link = "identity", sigma.link = "log", nu.link = "log",
tau.link = "log")
dSEP4(x, mu = 0, sigma = 1, nu = 2, tau = 2, log = FALSE)
pSEP4(q, mu = 0, sigma = 1, nu = 2, tau = 2, lower.tail = TRUE,
log.p = FALSE)
qSEP4(p, mu = 0, sigma = 1, nu = 2, tau = 2, lower.tail = TRUE,
log.p = FALSE)
rSEP4(n, mu = 0, sigma = 1, nu = 2, tau = 2)
mu.link
, with "identity" link as the default for the mu
parameter. Other links are "inverse" and "log"sigma.link
, with "log" link as the default for the sigma
parameter. Other links are "inverse" and "identity"nu.link
, with "log" link as the default for the nu
parameter. Other links are "identity" and "inverse"tau.link
, with "log" link as the default for the tau
parameter. Other links are "inverse", and "identitynu
parameter valuestau
parameter valueslength(n) > 1
, the length is
taken to be the number requiredSEP2()
returns a gamlss.family
object which can be used to fit the SEP2 distribution in the gamlss()
function.
dSEP2()
gives the density, pSEP2()
gives the distribution
function, qSEP2()
gives the quantile function, and rSEP2()
generates random deviates.SEP2
), is defined as
$$f_Y(y|\mu,\sigma\,\nu,\tau)=\frac{\nu}{\sigma (1+\nu^2)2^{1/\tau} \Gamma(1+1/\tau)}\left{\exp\left(- \frac{1}{2} \left|\frac{\nu (y-\mu)}{\sigma} \right|^\tau \right) I(y<\mu)+\exp\left(- \frac{1}{2}="" \left|\frac{(y-\mu)}{\sigma="" \nu}="" \right|^\tau="" \right)="" i(y="" \geq="" \mu)\right}$$<="" p="">for $-\infty < y < \infty$, $\mu=(-\infty,+\infty)$, $\sigma>0$, $\nu>0)$ and $\tau>0$.
\mu)+\exp\left(->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
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,
gamlss.family
, SEP
SEP1()
curve(dSEP4(x, mu=5 ,sigma=1, nu=2, tau=1.5), -2, 10,
main = "The SEP4 density mu=5 ,sigma=1, nu=1, tau=1.5")
# library(gamlss)
#y<- rSEP4(100, mu=5, sigma=1, nu=2, tau=1.5);hist(y)
#m1<-gamlss(y~1, family=SEP1, n.cyc=50)
#m2<-gamlss(y~1, family=SEP2, n.cyc=50)
#m3<-gamlss(y~1, family=SEP3, n.cyc=50)
#m4<-gamlss(y~1, family=SEP4, n.cyc=50)
#GAIC(m1,m2,m3,m4)
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