Zipf {VGAM} | R Documentation

## The Zipf Distribution

### Description

Density, distribution function, quantile function and random generation for the Zipf distribution.

### Usage

    dzipf(x, N, shape, log = FALSE)
    pzipf(q, N, shape, log.p = FALSE)
    qzipf(p, N, shape)
    rzipf(n, N, shape)

### Arguments

`x, q, p, n` | Same as `Poisson`.
`N, shape` | the number of elements, and the exponent characterizing the distribution. See `zipf` for more details.
`log, log.p` | Same meaning as in `Normal`.

### Details

This is a finite version of the zeta distribution. See `zetaff` for more details. In general, these functions runs slower and slower as `N` increases.

### Value

`dzipf` gives the density, `pzipf` gives the cumulative distribution function, `qzipf` gives the quantile function, and `rzipf` generates random deviates.

### Author(s)

T. W. Yee

### See Also

`zipf`.

### Examples

    N <- 10; shape <- 0.5; y <- 1:N
    proby <- dzipf(y, N = N, shape = shape)
    ## Not run:  plot(proby ~ y, type = "h", col = "blue", ylab = "Probability",
         ylim = c(0, 0.2), main = paste("Zipf(N = ",N,", shape = ",shape,")", sep = ""),
         lwd = 2, las = 1)
    ## End(Not run)
    sum(proby)  # Should be 1
    max(abs(cumsum(proby) - pzipf(y, N = N, shape = shape)))  # Should be 0

[Package VGAM version 1.0-3 Index]