Zipf {VGAM}

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, Zipfmb.

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",
   ylim = c(0, 0.2), ylab = "Probability", lwd = 2, las = 1,
   main = paste0("Zipf(N = ", N, ", shape = ", shape, ")")) 
## End(Not run)
sum(proby)  # Should be 1
max(abs(cumsum(proby) - pzipf(y, N = N, shape = shape)))  # 0?