VGAM (version 0.7-1)

posbinomial: Positive Binomial Distribution Family Function

Description

Fits a positive binomial distribution.

Usage

posbinomial(link = "logit")

Arguments

link

Link function for the usual probability parameter. See Links for more choices.

Value

• An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, rrvglm and vgam.

Warning

Under- or over-flow may occur if the data is ill-conditioned.

Details

The positive binomial distribution is the ordinary binomial distribution but with the probability of zero being zero. Thus the other probabilities are scaled up (i.e., divided by 1-P(Y=0)).

References

Patil, G. P. (1962) Maximum likelihood estimation for generalised power series distributions and its application to a truncated binomial distribution. Biometrika, 49, 227--237.

Documentation accompanying the VGAM package at http://www.stat.auckland.ac.nz/~yee contains further information and examples.

See Also

binomialff.

Examples

# Number of albinotic children in families with 5 children
# Data from Patil (1962) 
y = c(rep(1,25), rep(2,23), rep(3,10), 4, 5)  # No zeros 
n = rep(5, 60)
yprop = y / 5
# Fit the identical models in two ways; MLE of p is 0.3088 
fit = vglm(yprop ~ 1, posbinomial, trace=TRUE, weights=n)
fit2 = vglm(cbind(y, n-y) ~ 1, posbinomial, trace=TRUE)
summary(fit)
summary(fit2)
Coef(fit2)   # = MLE of p
Coef(fit)    # = MLE of p
fitted(fit2)[1:2]
fitted(fit)[1:2]