Otzeta {VGAM} | 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

### See Also

`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 distribution: blue=PMF; orange=CDF")
    lines(x + 0.1, potzeta(x, shape = shape), col = "orange", lty = 3, type = "h")
    ## End(Not run)

[Package VGAM version 1.1-1 Index]