VGAM (version 1.1-1)

oizipf: One-inflated Zipf Distribution Family Function

Description

Fits a 1-inflated Zipf distribution.

Usage

oizipf(N = NULL, lpstr1 = "logitlink", lshape = "loglink",
  type.fitted = c("mean", "shape", "pobs1", "pstr1", "onempstr1"),
  ishape = NULL, gpstr1 = ppoints(8), gshape = exp((-3:3) / 4), zero = NULL)

Arguments

N

Same as zipf.

lpstr1, lshape

For lpstr1: the same idea as zipoisson except it applies to a structural 1.

gpstr1, gshape, ishape

For initial values. See CommonVGAMffArguments for information.

type.fitted, zero

See CommonVGAMffArguments for information.

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. Lots of data is needed to estimate the parameters accurately. Usually, probably the shape parameter is best modelled as intercept-only.

Details

The 1-inflated Zipf distribution is a mixture distribution of the Zipf distribution with some probability of obtaining a (structural) 1. Thus there are two sources for obtaining the value 1. This distribution is written here in a way that retains a similar notation to the zero-inflated Poisson, i.e., the probability \(P[Y=1]\) involves another parameter \(\phi\). See zipoisson.

This family function can handle multiple responses.

See Also

Oizipf. zipf, Oizeta.

Examples

# NOT RUN {
 odata <- data.frame(x2 = runif(nn <- 1000))  # Artificial data
odata <- transform(odata, pstr1 = logitlink(-1 + x2, inverse = TRUE),
                          myN   = 10,
                          shape = exp(-0.5))
odata <- transform(odata, y1 = roizipf(nn, N = myN, s = shape, pstr1 = pstr1))
with(odata, table(y1))
fit1 <- vglm(y1 ~ x2, oizipf(zero = "shape"), data = odata, trace = TRUE)
coef(fit1, matrix = TRUE)
# }