R: Differenced Zeta Distribution

Diffzeta {VGAM} | R Documentation

## Differenced Zeta Distribution

### Description

Density, distribution function, quantile function, and random generation for the differenced zeta distribution.

### Usage

    ddiffzeta(x, shape, start = 1, log = FALSE)
    pdiffzeta(q, shape, start = 1, lower.tail = TRUE)
    qdiffzeta(p, shape, start = 1)
    rdiffzeta(n, shape, start = 1)

### Arguments

`x, q, p, n` | Same as in `runif`.
`shape, start` | Details at `diffzeta`.
`log, lower.tail` | Same as in `runif`.

### Details

This distribution appears to work well on the distribution of English words in such texts. Some more details are given in `diffzeta`.

### Value

`ddiffzeta` gives the density, `pdiffzeta` gives the distribution function, `qdiffzeta` gives the quantile function, and `rdiffzeta` generates random deviates.

### Note

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

Function `pdiffzeta()` suffers from the problems that `plog` sometimes has, i.e., when `p` is very close to 1.

### Author(s)

T. W. Yee

### See Also

`diffzeta`, `zetaff`, `zipf`, `Oizeta`.

### Examples

    ddiffzeta(1:20, 0.5, start = 2)
    rdiffzeta(20, 0.5)

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

[Package VGAM version 1.1-3 Index]