R: The exponential generalized Beta type 2 distribution for...
EGB2
R Documentation
The exponential generalized Beta type 2 distribution for fitting a GAMLSS
Description
This function defines the generalized t distribution, a four parameter distribution. The response variable is
in the range from minus infinity to plus infinity.
The functions dEGB2,
pEGB2, qEGB2 and rEGB2 define the density,
distribution function, quantile function and random
generation for the generalized beta type 2 distribution.
Usage
EGB2(mu.link = "identity", sigma.link = "identity", nu.link = "log",
tau.link = "log")
dEGB2(x, mu = 0, sigma = 1, nu = 1, tau = 0.5, log = FALSE)
pEGB2(q, mu = 0, sigma = 1, nu = 1, tau = 0.5, lower.tail = TRUE,
log.p = FALSE)
qEGB2(p, mu = 0, sigma = 1, nu = 1, tau = 0.5, lower.tail = TRUE,
log.p = FALSE)
rEGB2(n, mu = 0, sigma = 1, nu = 1, tau = 0.5)
Arguments
mu.link
Defines the mu.link, with "identity" link as the default for the mu parameter.
sigma.link
Defines the sigma.link, with "log" link as the default for the sigma parameter.
nu.link
Defines the nu.link, with "log" link as the default for the nu parameter.
tau.link
Defines the tau.link, with "log" link as the default for the tau parameter.
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 Generalized Beta type 2, (GB2), is defined as
for -Inf<y<Inf, where z=(y-mu)/sigma and
-Inf<mu<Inf, -Inf<sigma<Inf,
nu>0 and tau>0, McDonald and Xu (1995).
Value
EGB2() returns a gamlss.family object which can be used to fit the EGB2 distribution in the
gamlss() function.
dEGB2() gives the density, pEGB2() gives the distribution
function, qEGB2() gives the quantile function, and rEGB2()
generates random deviates.
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.org/).
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.