Hzeta {VGAM}

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,\ldots.

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,
     sub = paste("shape =", shape), las = 1, col = "blue",
     ylab = "Probability", lwd = 2,
     main = "Haight's zeta: blue = density; orange = CDF")
lines(x+0.1, phzeta(x, shape = shape), col = "orange", lty = 3, lwd = 2,
      type = "h")

## End(Not run)