# oizipf: One-inflated Zipf Distribution Family Function In VGAMdata: Data Supporting the 'VGAM' Package

## Description

Fits a 1-inflated Zipf distribution.

## Usage

 ```1 2 3``` ```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.

Thomas W. Yee

## See Also

`Oizipf`. `zipf`, `Oizeta`.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```## 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) ## End(Not run) ```

VGAMdata documentation built on Jan. 16, 2021, 5:08 p.m.