Positive Poisson Distribution Family Function
Fits a positive Poisson distribution.
pospoisson(link = "loglink", type.fitted = c("mean", "lambda", "prob0"),
expected = TRUE, ilambda = NULL, imethod = 1, zero = NULL, gt.1 = FALSE)link |
Link function for the usual mean (lambda) parameter of
an ordinary Poisson distribution.
See |
expected |
Logical.
Fisher scoring is used if |
ilambda, imethod, zero |
See |
type.fitted |
See |
gt.1 |
Logical.
Enforce |
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.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm,
rrvglm and vgam.
Under- or over-flow may occur if the data is ill-conditioned.
This family function can handle multiple responses.
Yet to be done: a quasi.pospoisson which estimates a dispersion
parameter.
Thomas W. Yee
Coleman, J. S. and James, J. (1961). The equilibrium size distribution of freely-forming groups. Sociometry, 24, 36–45.
# 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 = rgaitpois(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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