R: Positive Poisson Distribution Family Function

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, imethod = 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.
`imethod`	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.

Examples

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

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

[Package VGAM version 0.8-4 Index]