VGAM (version 1.0-5)

pospoisson: Positive Poisson Distribution Family Function

Description

Fits a positive Poisson distribution.

Usage

pospoisson(link = "loge", type.fitted = c("mean", "lambda", "prob0"),
           expected = TRUE, ilambda = NULL, imethod = 1, zero = NULL)

Arguments

link

Link function 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, zero

See CommonVGAMffArguments for information.

type.fitted

See CommonVGAMffArguments for details.

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.

See Also

Pospois, posnegbinomial, poissonff, otpospoisson, zapoisson, zipoisson, simulate.vlm.

Examples

# NOT RUN {
# Data from Coleman and James (1961)
cjdata <- data.frame(y = 1:6, freq = c(1486, 694, 195, 37, 10, 1))
fit <- vglm(y ~ 1, pospoisson, data = cjdata, weights = freq)
Coef(fit)
summary(fit)
fitted(fit)

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