VGAM (version 0.8-3)

posbinomial: Positive Binomial Distribution Family Function

Description

Fits a positive binomial distribution.

Usage

posbinomial(link = "logit", earg = list(),
            mv = FALSE, parallel = FALSE, zero = NULL)

Arguments

link, earg

Link function and its extra argument for the usual probability parameter. See CommonVGAMffArguments for more information.

mv, parallel, zero

See CommonVGAMffArguments for more information.

Value

• An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, 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 $1-P(Y=0)$). The fitted values are the ordinary binomial distribution fitted values, i.e., the usual mean.

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 kids (from Patil, 1962)
akids = data.frame(y = c(rep(1, 25), rep(2, 23), rep(3, 10), 4, 5),
                   n = rep(5, 60))
fit1 = vglm(cbind(y, n-y) ~ 1, posbinomial, akids, trace = TRUE)
summary(fit1)
Coef(fit1)   # = MLE of p = 0.3088
head(fitted(fit1))