gamlss.dist (version 3.0-1)

BEINF: The beta inflated distribution for fitting a GAMLSS

Description

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.

Usage

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)

Arguments

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

Value

• returns a gamlss.family object which can be used to fit a beta inflated distribution in the gamlss() function. ...

Details

The beta inflated distribution is given as $$f(y)=p_0$$ if (y=0) $$f(y)=p_1$$ if (y=1) $$f(y|\alpha,\beta)=\frac{1}{B(\alpha, \beta)} y^{\alpha-1}(1-y)^{\beta-1}$$ otherwise for $y=(0,1)$, $\alpha>0$ and $\beta>0$. The parametrization in the function BEINF() is $\mu=\frac{\alpha}{\alpha+\beta}$ and $\sigma=\frac{1}{\alpha+\beta+1}$ for $\mu=(0,1)$ and $\sigma=(0,1)$ and $\nu=\frac{p_0}{p_2}$, $\tau=\frac{p_1}{p_2}$ where $p_2=1-p_0-p_1$.

References

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.

See Also

gamlss.family, BE

Examples

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]