Zeta {VGAM} | R Documentation

## 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.

### Details

The density function of the zeta distribution is given by

y^(-p-1) / zeta(p+1)

where p>0, y=1,2,…, and zeta is Riemann's zeta function.

### Value

Returns the density evaluated at `x`.

### Warning

This function has not been fully tested.

### Note

The VGAM family function `zetaff` estimates the parameter p.

### Author(s)

T. W. Yee

### 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)

[Package VGAM version 1.0-1 Index]