The ex-Gaussian distribution is often used by psychologists to model response time (RT). It is defined by adding two
random variables, one from a normal distribution and the other from an exponential. The parameters mu and
sigma are the mean and standard deviation from the normal distribution variable while the parameter nu
is the mean of the exponential variable.
The functions dexGAUS, pexGAUS, qexGAUS and rexGAUS define the density, distribution function,
quantile function and random generation for the ex-Gaussian distribution.
Usage
exGAUS(mu.link = "identity", sigma.link = "log", nu.link = "log")
dexGAUS(x, mu = 5, sigma = 1, nu = 1, log = FALSE)
pexGAUS(q, mu = 5, sigma = 1, nu = 1, lower.tail = TRUE, log.p = FALSE)
qexGAUS(p, mu = 5, sigma = 1, nu = 1, lower.tail = TRUE, log.p = FALSE)
rexGAUS(n, mu = 5, sigma = 1, nu = 1, ...)
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.
Other links are "inverse", "identity", "logshifted" (shifted from one) and "own"
x,q
vector of quantiles
mu
vector of mu parameter values
sigma
vector of scale parameter values
nu
vector of nu 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
...
for extra arguments
Details
The probability density function of the ex-Gaussian distribution, (exGAUS), is defined as
where Phi is the cdf of the standard normal distribution,
for -Inf<y<Inf, -Inf<mu<Inf, σ>0 and ν>0.
Value
exGAUS() returns a gamlss.family object which can be used to fit ex-Gaussian distribution in the gamlss() function.
dexGAUS() gives the density, pexGAUS() gives the distribution function,
qexGAUS() gives the quantile function, and rexGAUS()
generates random deviates.
Note
The mean of the ex-Gaussian is mu+nu and the variance is sigma^2+nu^2.
Author(s)
Mikis Stasinopoulos and Bob Rigby
References
Cousineau, D. Brown, S. and Heathecote A. (2004) Fitting distributions using maximum likelihood: Methods and packages,
Behavior Research Methods, Instruments and Computers, 46, 742-756.
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.
See Also
gamlss.family, BCCG, GA,
IGLNO
Examples
exGAUS() #
y<- rexGAUS(100, mu=300, nu=100, sigma=35)
hist(y)
# library(gamlss)
# m1<-gamlss(y~1, family=exGAUS)
# plot(m1)
curve(dexGAUS(x, mu=300 ,sigma=35,nu=100), 100, 600,
main = "The ex-GAUS density mu=300 ,sigma=35,nu=100")
plot(function(x) pexGAUS(x, mu=300,sigma=35,nu=100), 100, 600,
main = "The ex-GAUS cdf mu=300, sigma=35, nu=100")