SEP {gamlss.dist} | R Documentation |
This function defines the Skew Power exponential (SEP) distribution, a four parameter distribution,
for a gamlss.family
object to be used for a
GAMLSS fitting using the function gamlss()
. The functions dSEP
,
pSEP
, qSEP
and rSEP
define the density,
distribution function, quantile function and random
generation for the Skew Power exponential (SEP) distribution.
SEP(mu.link = "identity", sigma.link = "log", nu.link = "identity", tau.link = "log") dSEP(x, mu = 0, sigma = 1, nu = 0, tau = 2, log = FALSE) pSEP(q, mu = 0, sigma = 1, nu = 0, tau = 2, lower.tail = TRUE, log.p = FALSE) qSEP(p, mu = 0, sigma = 1, nu = 0, tau = 2, lower.tail = TRUE, log.p = FALSE, lower.limit = mu - 5 * sigma, upper.limit = mu + 5 * sigma) rSEP(n, mu = 0, sigma = 1, nu = 0, tau = 2)
mu.link |
Defines the mu.link , with "identity" link as the default for the mu parameter. Other links are "1/mu^2" and "log" |
sigma.link |
Defines the sigma.link , with "log" link as the default for the sigma parameter. Other links are "inverse" and "identity" |
nu.link |
Defines the nu.link , with "identity" link as the default for the nu parameter. Other links are "1/nu^2" and "log" |
tau.link |
Defines the tau.link , with "log" link as the default for the tau parameter. Other links are "1/tau^2", and "identity |
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 |
lower.limit |
lower limit for the golden search to find quantiles from probabilities |
upper.limit |
upper limit for the golden search to find quantiles from probabilities |
The probability density function of the Skew Power exponential distribution, (SEP
), is defined as
f(y|mu,sigma,nu,tau)=(z/sigma)*pnorm(w)*dPE(z,0,1,tau)
for 0<y<0, mu=(-Inf,+Inf), sigma>0, nu=(-Inf,+Inf) and tau>0. where z=(y-mu)/(sigma), w=sign(z)|z|^(t/2) *nu*sqrt(2/tau) and dPE(z,0,1,tau) is the pdf of an Exponential Power distribution.
SEP()
returns a gamlss.family
object which can be used to fit the SEP distribution in the gamlss()
function.
dSEP()
gives the density, pSEP()
gives the distribution
function, qSEP()
gives the quantile function, and rSEP()
generates random deviates.
The qSEP and rSEP are slow since they are relying on golden section for finding the quantiles
Bob Rigby r.rigby@londonmet.ac.uk and Mikis Stasinopoulos d.stasinopoulos@londonmet.ac.uk
Diciccio, T. J. and Mondi A. C. (2004). Inferential Aspects of the Skew Exponential Power distribution., JASA, 99, 439-450.
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.
SEP() # plot(function(x)dSEP(x, mu=0,sigma=1, nu=1, tau=2), -5, 5, main = "The SEP density mu=0,sigma=1,nu=1, tau=2") plot(function(x) pSEP(x, mu=0,sigma=1,nu=1, tau=2), -5, 5, main = "The BCPE cdf mu=0, sigma=1, nu=1, tau=2") dat <- rSEP(100,mu=10,sigma=1,nu=-1,tau=1.5) # library(gamlss) # gamlss(dat~1,family=SEP, control=gamlss.control(n.cyc=30))