# hzetaUC: Haight's Zeta Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```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

`hzeta`, `zeta`, `zetaff`, `simulate.vlm`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ```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) ```