pospoisson {VGAM}R Documentation

Positive Poisson Distribution Family Function

Description

Fits a positive Poisson distribution.

Usage

pospoisson(link = "loge", 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 more information.

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 a multivariate response.

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

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

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

[Package VGAM version 0.9-8 Index]