# zipfUC: The Zipf Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```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

`zipf`, `Zipfmb`.
 ```1 2 3 4 5 6 7 8``` ```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 ```