VGAM (version 1.0-2)

Zeta: The Zeta Distribution

Description

Density for the zeta distribution.

Usage

dzeta(x, p, log = FALSE)

Arguments

x

Numerical vector/matrix to evaluate the density.

p

The parameter $p$. This must be positive.

log

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

Value

Returns the density evaluated at x.

Warning

This function has not been fully tested.

Details

The density function of the zeta distribution is given by $$y^{-p-1} / \zeta(p+1)$$ where $p>0$, $y=1,2,\ldots$, and $zeta$ is Riemann's zeta function.

References

Johnson N. L., Kotz S., and Balakrishnan N. (1993) Univariate Discrete Distributions, 2nd ed. New York: Wiley.

See Also

zeta, zetaff.

Examples

dzeta(1:20, p = 2)
## Not run:  plot(1:6, dzeta(1:6, p = 4), type = "h", las = 1, ylab = "Probability",
#      main = "zeta probability function; black: p = 4; blue: p = 2")
# points(0.10 + 1:6, dzeta(1:6, p = 2), type = "h", col = "blue") ## End(Not run)