The BI() function defines the binomial distribution, a one parameter family distribution, for a gamlss.family object to be used
in GAMLSS fitting using the function gamlss().
The functions dBI, pBI, qBI and rBI define the density, distribution function, quantile function and random
generation for the binomial, BI(), distribution.
returns a gamlss.family object which can be used to fit a binomial distribution in the gamlss() function.
Note
The response variable should be a matrix containing two columns, the first with the count of successes and the second with the count of failures.
The parameter mu represents a probability parameter with limits 0 < mu <1.
n*mu is the mean of the distribution where n is the binomial denominator.
Author(s)
Mikis Stasinopoulos, Bob Rigby and Calliope Akantziliotou
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.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, ZABI, ZIBI
Examples
BI()# gives information about the default links for the Binomial distribution
# data(aep)
# library(gamlss)
# h<-gamlss(y~ward+loglos+year, family=BI, data=aep)
# plot of the binomial distribution
curve(dBI(x, mu = .5, bd=10), from=0, to=10, n=10+1, type="h")
tN <- table(Ni <- rBI(1000, mu=.2, bd=10))
r <- barplot(tN, col='lightblue')