VGAM (version 1.1-13)

Hzeta: 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)

Value

dhzeta gives the density,

phzeta gives the distribution function,

qhzeta gives the quantile function, and

rhzeta generates random deviates.

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.

Author

T. W. Yee and Kai Huang

Details

The probability function is $$f(x)=(2x-1{)}^{(-\alpha )}-(2x+1{)}^{(-\alpha )},$$ where $\alpha >0$ and $x=1,2,\dots$.

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))

if (FALSE)  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")