Hzeta {VGAM} | R Documentation

## Haight's Zeta Distribution

### Description

Density, distribution function, quantile function and random generation for Haight's zeta distribution with parameter `shape`.

### Usage

    dhzeta(x, shape, log = FALSE)
    phzeta(q, shape, log.p = FALSE)
    qhzeta(p, shape)
    rhzeta(n, shape)

### Arguments

`x, q, p, n` | Same meaning as `runif`.
`shape` | The positive shape parameter. Called alpha below.
`log,log.p` | Same meaning as in `pnorm` or `qnorm`.

### Details

The probability function is

f(x) = (2x-1)^(-alpha) - (2x+1)^(-alpha),

where alpha>0 and x=1,2,....

### Value

`dhzeta` gives the density, `phzeta` gives the distribution function, `qhzeta` gives the quantile function, and `rhzeta` generates random deviates.

### Note

Given some response data, the VGAM family function `hzeta` estimates the parameter `shape`.

### Author(s)

T. W. Yee and Kai Huang

### See Also

`hzeta`, `zeta`, `zetaff`, `simulate.vlm`.

### Examples

    dhzeta(1:20, 2.1)
    rhzeta(20, 2.1)

    round(1000 * dhzeta(1:8, 2))
    table(rhzeta(1000, 2))

    ## Not run:  shape <- 1.1; x <- 1:10
    plot(x, dhzeta(x, shape = shape), type = "h", ylim = 0:1, lwd = 2,
         sub = paste("shape =", shape), las = 1, col = "blue", ylab = "Probability",
         main = "Haight's zeta: blue = density; orange = distribution function")
    lines(x+0.1, phzeta(x, shape = shape), col = "orange", lty = 3, lwd = 2,
          type = "h")

    ## End(Not run)

[Package VGAM version 1.1-1 Index]