The function EXP defines the exponential distribution, a one parameter distribution for a
gamlss.family object to be used in GAMLSS fitting using the function gamlss().
The mu parameter represents the mean of the distribution.
The functions dEXP, pEXP, qEXP and rEXP define the density,
distribution function, quantile function and random generation for the specific parameterization
of the exponential distribution defined by function EXP.
Usage
EXP(mu.link ="log")
dEXP(x, mu = 1, log = FALSE)
pEXP(q, mu = 1, lower.tail = TRUE, log.p = FALSE)
qEXP(p, mu = 1, lower.tail = TRUE, log.p = FALSE)
rEXP(n, mu = 1)
Arguments
mu.link
Defines the mu.link, with "log" link as the default for the mu parameter, other links are "inverse" and "identity"
x,q
vector of quantiles
mu
vector of location 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 specific parameterization of the exponential distribution used in EXP is
f(y|mu)=1/mu*exp(-y/mu)
,
for y>0, mu>0.
Value
EXP() returns a gamlss.family object which can be used to fit an exponential distribution in
the gamlss() function. dEXP() gives the density, pEXP() gives the distribution function, qEXP() gives the quantile function,
and rEXP() 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.