pospoisson {VGAM} | R Documentation

## Positive Poisson Distribution Family Function

### Description

Fits a positive Poisson distribution.

### Usage

    pospoisson(link = "loge", earg=list(),
               expected=TRUE, ilambda=NULL, method.init=1)

### Arguments

`link` | Link function for the usual mean (lambda) parameter of an ordinary Poisson distribution. See `Links` for more choices.
`earg` | List. Extra argument for the link. See `earg` in `Links` for general information.
`expected` | Logical. Fisher scoring is used if `expected = TRUE`, else Newton-Raphson.
`ilambda` | Optional initial value for lambda. A `NULL` means a value is computed internally.
`method.init` | An integer with value `1` or `2` or `3` which specifies the initialization method for lambda. If failure to converge occurs try another value and/or else specify a value for `ilambda`.

### Details

The positive Poisson distribution is the ordinary Poisson 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 mean, lambda/(1-exp(-lambda)), can be obtained by the extractor function `fitted` applied to the object.

A related distribution is the zero-inflated Poisson, in which the probability P[Y=0] involves another parameter phi. See `zipoisson`.

### 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

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

This family function can handle a multivariate response.

### Author(s)

Thomas W. Yee

### References

Coleman, J. S. and James, J. (1961) The equilibrium size distribution of freely-forming groups. Sociometry, 24, 36–45.

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

### See Also

`Pospois`, `posnegbinomial`, `poissonff`, `zipoisson`.

### Examples

    y = 1:6
    w = c(1486, 694, 195, 37, 10, 1) # Data from Coleman and James (1961)
    fit = vglm(y ~ 1, pospoisson, weights=w)
    Coef(fit)
    summary(fit)
    fitted(fit)

    # Artificial data
    x = runif(n <- 1000)
    lambda = exp(1 - 2*x)
    y = rpospois(n, lambda)
    table(y)
    fit = vglm(y ~ x, pospoisson, trace=TRUE, crit="c")
    coef(fit, matrix=TRUE)

[Package VGAM version 0.7-9 Index]