The Zeta Distribution
Density, distribution function, quantile function and random generation for the zeta distribution.
dzeta(x, shape, log = FALSE) pzeta(q, shape, lower.tail = TRUE) qzeta(p, shape) rzeta(n, shape)
The density function of the zeta distribution is given by
y^(-s-1) / zeta(s+1)
where s>0, y=1,2,…, and zeta is Riemann's zeta function.
dzeta gives the density,
pzeta gives the distribution function,
qzeta gives the quantile function, and
rzeta generates random deviates.
qzeta() runs slower and slower as shape approaches 0
and p approaches 1.
The VGAM family function zetaff estimates the
shape parameter s.
T. W. Yee
Johnson N. L., Kotz S., and Balakrishnan N. (1993). Univariate Discrete Distributions, 2nd ed. New York: Wiley.
dzeta(1:20, shape = 2)
myshape <- 0.5
max(abs(pzeta(1:200, myshape) -
cumsum(1/(1:200)^(1+myshape)) / zeta(myshape+1))) # Should be 0
## Not run: plot(1:6, dzeta(1:6, 2), type = "h", las = 1,
col = "orange", ylab = "Probability",
main = "zeta probability function; orange: shape = 2; blue: shape = 1")
points(0.10 + 1:6, dzeta(1:6, 1), type = "h", col = "blue")
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.