gamlss.dist: SEP1 – R documentation

Become an expert in R — Interactive courses, Cheat Sheets, certificates and more!

SEP1

The Skew Power exponential type 1-4 distribution for fitting a GAMLSS

Description

These functions define the Skew Power exponential type 1 to 4 distributions. All of them are four parameter distributions and can be used to fit a GAMLSS model. The functions 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.

Usage

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)

Arguments

`mu.link`	Defines the `mu.link`, with "identity" link as the default for the `mu` parameter. Other links are "inverse" 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 "log" link as the default for the `nu` parameter. Other links are "identity" and "inverse"
`tau.link`	Defines the `tau.link`, with "log" link as the default for the `tau` parameter. Other links are "inverse", 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

Details

The probability density function of the Skew Power exponential distribution type 2, (SEP2), is defined as

f(y|mu,sigma,nu,tau)=nu/(sigma*(1+nu^2)*2^(1/tau) Gamma(1+1/tau))*(exp(-.5*abs(nu(y-mu)/sigma))^tau*I(y<mu)+exp(-.5*abs((y-mu)/sigma*nu))^tau*I(y>=mu))

for 0<y<0, mu=(-Inf,+Inf), sigma>0, nu>0) and tau>0.

Value

SEP2() 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.

Author(s)

Bob Rigby and Mikis Stasinopoulos

References

Fernadez C., Osiewalski J. and Steel M.F.J.(1995) Modelling and inference with v-spherical distributions. JASA, 90, pp 1331-1340.

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. 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, https://www.jstatsoft.org/v23/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.

Examples

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)

gamlss.dist

Distributions for Generalized Additive Models for Location Scale and Shape

v5.3-2

GPL-2 | GPL-3

Authors

Mikis Stasinopoulos [aut, cre, cph], Robert Rigby [aut], Calliope Akantziliotou [ctb], Vlasios Voudouris [ctb], Gillian Heller [ctb], Fernanda De Bastiani [ctb], Raydonal Ospina [ctb], Nicoletta Motpan [ctb], Fiona McElduff [ctb], Majid Djennad [ctb], Marco Enea [ctb], Alexios Ghalanos [ctb], Christos Argyropoulos [ctb], Almond Stocker [ctb], Jens Lichter [ctb], Stanislaus Stadlmann [ctb]

Initial release

2021-03-08