BEINF {gamlss.dist} | R Documentation |
The function BEINF()
defines the beta inflated distribution, a four parameter distribution, for a
gamlss.family
object to be used in GAMLSS fitting
using the function gamlss()
. The beta inflated is similar to the beta but allows zeros and one as y values. The two extra parameters model
the probabilities at zero and one.
The functions dBEINF
, pBEINF
, qBEINF
and rBEInF
define the density, distribution function, quantile function and random
generation for the BEINF
parameterization of the beta inflated distribution.
plotBEINF
can be used to plot the distribution. meanBEINF
calculates the expected value of the response for a fitted model.
BEINF(mu.link = "logit", sigma.link = "logit", nu.link = "log", tau.link = "log") dBEINF(x, mu = 0.5, sigma = 0.1, nu = 0.1, tau = 0.1, log = FALSE) pBEINF(q, mu = 0.5, sigma = 0.1, nu = 0.1, tau = 0.1, lower.tail = TRUE, log.p = FALSE) qBEINF(p, mu = 0.5, sigma = 0.1, nu = 0.1, tau = 0.1, lower.tail = TRUE, log.p = FALSE) rBEINF(n, mu = 0.5, sigma = 0.1, nu = 0.1, tau = 0.1) plotBEINF(mu = 0.5, sigma = 0.5, nu = 0.5, tau = 0.5, from = 0.001, to = 0.999, n = 101, ...) meanBEINF(obj)
mu.link |
the mu link function with default logit |
sigma.link |
the sigma link function with default logit |
nu.link |
the nu link function with default log |
tau.link |
the tau link function with default log |
x,q |
vector of quantiles |
mu |
vector of location parameter values |
sigma |
vector of scale parameter values |
nu |
vector of parameter values modelling the probability at zero |
tau |
vector of parameter values modelling the probability at one |
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 |
from |
where to start plotting the distribution from |
to |
up to where to plot the distribution |
obj |
a fitted BEINF object |
... |
other graphical parameters for plotting |
The beta inflated distribution is given as
f(y)=p0
if (y=0)
f(y)=p1
if (y=1)
f(y|a,b)=(1/(Beta(a,b))) y^(a-1)(1-y)^(b-1)
otherwise
for y=(0,1), α>0 and β>0. The parametrization in the function BEINF()
is
mu=a/(a+b) and sigma=1/(a+b+1)
for mu=(0,1) and sigma=(0,1) and nu=p0/p2,
tau=p1/p2 where p2=1-p0-p1.
returns a gamlss.family
object which can be used to fit a beta inflated 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.
BEINF()# gives information about the default links for the normal distribution # plotting the distribution plotBEINF( mu =.5 , sigma=.5, nu = 0.5, tau = 0.5, from = 0, to=1, n = 101) # plotting the cdf plot(function(y) pBEINF(y, mu=.5 ,sigma=.5, nu = 0.5, tau = 0.5,), 0, 1) # plotting the inverse cdf plot(function(y) qBEINF(y, mu=.5 ,sigma=.5, nu = 0.5, tau = 0.5,), 0.01, .99) # generate random numbers dat <- rBEINF(1000,mu=.5,sigma=.5, nu=.5, tau=.5) # fit a model to the data # library(gamlss) #m1<-gamlss(dat~1,family=BEINF) #meanBEINF(m1)[1]