VGAM (version 0.8-1)

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="P[Y=y]", 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