VGAM (version 1.1-9)

Diffzeta: Differenced Zeta Distribution

Description

Density, distribution function, quantile function, and random generation for the differenced zeta distribution.

Usage

ddiffzeta(x, shape, start = 1, log = FALSE)
pdiffzeta(q, shape, start = 1, lower.tail = TRUE)
qdiffzeta(p, shape, start = 1)
rdiffzeta(n, shape, start = 1)

Value

ddiffzeta gives the density,

pdiffzeta gives the distribution function,

qdiffzeta gives the quantile function, and

rdiffzeta generates random deviates.

Arguments

x, q, p, n

Same as in runif.

shape, start

Details at diffzeta.

log, lower.tail

Same as in runif.

Author

T. W. Yee

Details

This distribution appears to work well on the distribution of English words in such texts. Some more details are given in diffzeta.

See Also

diffzeta, zetaff, zipf, Oizeta.

Examples

ddiffzeta(1:20, 0.5, start = 2)
rdiffzeta(20, 0.5)

if (FALSE)  shape <- 0.8; x <- 1:10
plot(x, ddiffzeta(x, sh = shape), type = "h", ylim = 0:1, las = 1,
     sub = "shape=0.8", col = "blue", ylab = "Probability",
     main = "Differenced zeta distribution: blue=PMF; orange=CDF")
lines(x + 0.1, pdiffzeta(x, shape = shape), col = "orange",
      lty = 3, type = "h")