# otzetaUC: One-truncated Zeta Distribution In VGAMdata: Data Supporting the 'VGAM' Package

 Otzeta R Documentation

## One-truncated Zeta Distribution

### Description

Density, distribution function, quantile function, and random generation for the one-truncated zeta distribution.

### Usage

``````dotzeta(x, shape, log = FALSE)
potzeta(q, shape, log.p = FALSE)
qotzeta(p, shape)
rotzeta(n, shape)
``````

### Arguments

 `x, q, p, n` Same as in `runif`. `shape` The positive shape parameter described in in `zetaff`. Here it is called `shape` because it is positive. `log, log.p` Same as in `runif`.

### Details

The one-truncated zeta distribution is a zeta distribution but with the probability of a one being zero. The other probabilities are scaled to add to unity. Some more details are given in `zetaff`.

### Value

`dotzeta` gives the density, `potzeta` gives the distribution function, `qotzeta` gives the quantile function, and `rotzeta` generates random deviates.

### Note

Given some response data, the VGAM family function `otzeta` estimates the parameter `shape`.

### Author(s)

T. W. Yee

`Otzeta`, `zetaff`, `Oizeta`.

### Examples

``````dotzeta(1:20, 0.5)
rotzeta(20, 0.5)

## Not run:  shape <- 0.8; x <- 1:10
plot(x, dotzeta(x, shape = shape), type = "h", ylim = 0:1,
sub = "shape=0.8", las = 1, col = "blue", ylab = "Probability",
main = "1-truncated zeta distn: blue=PMF; orange=CDF")
lines(x + 0.1, potzeta(x, shape), col = "orange", lty = 3, type = "h")
## End(Not run)
``````

VGAMdata documentation built on Sept. 18, 2023, 9:08 a.m.