posbinomial {VGAM}R Documentation

Positive Binomial Distribution Family Function

Description

Fits a positive binomial distribution.

Usage

posbinomial(link = "logit", earg=list())

Arguments

link Link function for the usual probability parameter. See Links for more choices.
earg List. Extra argument for the link. See earg in Links for general information.

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)).

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.

Note

The input for this family function is the same as binomialff.

Yet to be done: a quasi.posbinomial which estimates a dispersion parameter.

Author(s)

Thomas W. Yee

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]

[Package VGAM version 0.7-7 Index]