VGAM: hzetaUC – R documentation

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hzetaUC

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

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)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13