VGAM (version 1.1-12)

Zipf: 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)

Value

dzipf gives the density,

pzipf gives the cumulative distribution function,

qzipf gives the quantile function, and

rzipf generates random deviates.

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.

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, ")")) 
sum(proby)  # Should be 1
max(abs(cumsum(proby) - pzipf(y, N = N, shape = shape)))  # 0?