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
    head(fitted(fit2))
    head(fitted(fit))

[Package VGAM version 0.7-9 Index]