pospoisson {VGAM}

Positive Poisson Distribution Family Function

Description

Fits a positive Poisson distribution.

Usage

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

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.

gt.1

Logical. Enforce lambda > 1? The default is to enforce lambda > 0.

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

This family function can handle multiple responses.

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

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.

See Also

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

Examples

# 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 = rgaitdpois(nn, lambda, truncate = 0))
with(pdata, table(y1))
fit <- vglm(y1 ~ x2, pospoisson, data = pdata, trace = TRUE, crit = "coef")
coef(fit, matrix = TRUE)