VGAM (version 0.8-7)

pospoisson: 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, earg

Link function and extra argument for the usual mean (lambda) parameter of an ordinary Poisson distribution. See Links for more choices.

expected

Logical. Fisher scoring is used if expected = TRUE, else Newton-Raphson.

ilambda, imethod

See CommonVGAMffArguments for more information.

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.

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.

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

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

pdat = data.frame(x2 = runif(nn <- 1000)) # Artificial data
pdat = transform(pdat, lambda = exp(1 - 2 * x2))
pdat = transform(pdat, y1 = rpospois(nn, lambda))
with(pdat, table(y1))
fit = vglm(y1 ~ x2, pospoisson, pdat, trace = TRUE, crit = "coef")
coef(fit, matrix=TRUE)