VGAM (version 0.8-4.1)

Zipf: The Zipf Distribution

Description

Density, and cumulative distribution function for the Zipf distribution.

Usage

dzipf(x, N, s, log = FALSE)
pzipf(q, N, s)

Arguments

x, q

vector of quantiles.

N, s

the number of elements, and the exponent characterizing the distribution. See zipf for more details.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Value

• dzipf gives the density, and pzipf gives the cumulative distribution function.

Details

This is a finite version of the zeta distribution. See zipf for more details.

See Also

zipf.

Examples

N = 10; s = 0.5; y = 1:N
proby = dzipf(y, N = N, s = s)
plot(proby ~ y, type = "h", col = "blue", ylab = "Probability",
     ylim = c(0, 0.2), main = paste("Zipf(N = ",N,", s = ",s,")", sep = ""),
     lwd = 2, las = 1)
sum(proby)  # Should be 1
max(abs(cumsum(proby) - pzipf(y, N = N, s = s))) # Should be 0