VGAM (version 1.1-6)

# pospoisson: Positive Poisson Distribution Family Function

## Description

Fits a positive Poisson distribution.

## Usage

expected = TRUE, ilambda = NULL, imethod = 1, zero = NULL, gt.1 = FALSE)

## Arguments

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.

## 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.

## Examples

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

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