otzetaUC: One-truncated Zeta Distribution

OtzetaR Documentation

One-truncated Zeta Distribution


Density, distribution function, quantile function, and random generation for the one-truncated zeta distribution.


dotzeta(x, shape, log = FALSE)
potzeta(q, shape, log.p = FALSE)
qotzeta(p, shape)
rotzeta(n, shape)


x, q, p, n

Same as in runif.


The positive shape parameter described in in zetaff. Here it is called shape because it is positive.

log, log.p

Same as in runif.


The one-truncated zeta distribution is a zeta distribution but with the probability of a one being zero. The other probabilities are scaled to add to unity. Some more details are given in zetaff.


dotzeta gives the density, potzeta gives the distribution function, qotzeta gives the quantile function, and rotzeta generates random deviates.


Given some response data, the VGAM family function otzeta estimates the parameter shape.


T. W. Yee

See Also

Otzeta, zetaff, Oizeta.


dotzeta(1:20, 0.5)
rotzeta(20, 0.5)

## Not run:  shape <- 0.8; x <- 1:10
plot(x, dotzeta(x, shape = shape), type = "h", ylim = 0:1,
     sub = "shape=0.8", las = 1, col = "blue", ylab = "Probability",
     main = "1-truncated zeta distn: blue=PMF; orange=CDF")
lines(x + 0.1, potzeta(x, shape), col = "orange", lty = 3, type = "h") 
## End(Not run)

VGAMdata documentation built on Sept. 18, 2023, 9:08 a.m.