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 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 0.7-7 Index]