oizipf: One-inflated Zipf Distribution Family Function

In VGAMdata: Data Supporting the 'VGAM' Package

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.

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.

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.

Author(s)

Thomas W. Yee

See Also

Oizipf. zipf, Oizeta.

Examples

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

## End(Not run)

VGAMdata documentation built on Sept. 17, 2024, 9:09 a.m.