The Zipf Distribution

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

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.

Value

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

Author

T. W. Yee

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.

See also

zipf, Zipfmb.

Examples

N <- 10; shape <- 0.5; y <- 1:N
proby <- dzipf(y, N = N, shape = shape)
if (FALSE)  plot(proby ~ y, type = "h", col = "blue",
   ylim = c(0, 0.2), ylab = "Probability", lwd = 2, las = 1,
   main = paste0("Zipf(N = ", N, ", shape = ", shape, ")"))  # \dontrun{}
sum(proby)  # Should be 1
#> [1] 1
max(abs(cumsum(proby) - pzipf(y, N = N, shape = shape)))  # 0?
#> [1] 1.110223e-16