ZAGA {gamlss.dist} | R Documentation |
The function ZAGA()
defines the zero adjusted Gamma distribution, a three parameter distribution, for a
gamlss.family
object to be used in GAMLSS fitting using the function gamlss()
.
The zero adjusted Gamma distribution is similar to the Gamma distribution
but allows zeros as y values. The extra parameter nu
models
the probabilities at zero.
The functions dZAGA
, pZAGA
, qZAGA
and rZAGA
define the density, distribution function,
quartile function and random
generation for the ZAGA
parameterization of the zero adjusted Gamma distribution.
plotZAGA
can be used to plot the distribution. meanZAGA
calculates the expected value of the response for a fitted model.
ZAGA(mu.link = "log", sigma.link = "log", nu.link = "logit") dZAGA(x, mu = 1, sigma = 1, nu = 0.1, log = FALSE) pZAGA(q, mu = 1, sigma = 1, nu = 0.1, lower.tail = TRUE, log.p = FALSE) qZAGA(p, mu = 1, sigma = 1, nu = 0.1, lower.tail = TRUE, log.p = FALSE, upper.limit = mu + 10 * sqrt(sigma^2 * mu^2)) rZAGA(n, mu = 1, sigma = 1, nu = 0.1, ...) plotZAGA(mu = 5, sigma = 1, nu = 0.1, from = 0, to = 10, n = 101, ...) meanZAGA(obj)
mu.link |
Defines the mu.link , with "log" 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 "logit" link as the default for the sigma parameter |
x,q |
vector of quantiles |
mu |
vector of location parameter values |
sigma |
vector of scale parameter values |
nu |
vector of probability at zero 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] |
upper.limit |
the argument upper.limit sets the upper limit in the golden section search for q,
the default is 10 time its standard deviation |
p |
vector of probabilities. |
n |
number of observations. If length(n) > 1 , the length is
taken to be the number required |
from |
where to start plotting the distribution from |
to |
up to where to plot the distribution |
obj |
a fitted gamlss object |
... |
... can be used to pass the uppr.limit argument to qIG |
The Zero adjusted GA distribution is given as
f(y|mu,sigma,nu)=nu
if (y=0)
f(y|mu,sigma,nu)=(1-nu)*(y^((1/sigma^2)-1)*exp[-y/((sigma^2)*mu)])/((sigma^2*mu)^(1/sigma^2) Gamma(1/sigma^2))
otherwise
for y=(0,Inf), mu>0, sigma>0 and 0<nu<1. E(y)=(1-nu)*mu and Var(y)=(1-nu)*mu^2*(nu+sigma^2).
The function ZAGA
returns a gamlss.family
object which can be used to fit a
zero adjusted Gamma distribution in the gamlss()
function.
Bob Rigby and Mikis Stasinopoulos
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.
ZAGA()# gives information about the default links for the ZAGA distribution # plotting the function PPP <- par(mfrow=c(2,2)) plotZAGA(mu=1, sigma=.5, nu=.2, from=0,to=3) #curve(dZAGA(x,mu=1, sigma=.5, nu=.2), 0,3) # pdf curve(pZAGA(x,mu=1, sigma=.5, nu=.2), 0,3, ylim=c(0,1)) # cdf curve(qZAGA(x,mu=1, sigma=.5, nu=.2), 0,.99) # inverse cdf y<-rZAGA(100, mu=1, sigma=.5, nu=.2) # randomly generated values hist(y) par(PPP) # check that the positive part sums up to .8 (since nu=0.2) integrate(function(x) dZAGA(x,mu=1, sigma=.5, nu=.2), 0,Inf)