otlogUC: One-truncated Logarithmic Distribution

OtlogR Documentation

One-truncated Logarithmic Distribution


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


dotlog(x, shape, log = FALSE)
potlog(q, shape, log.p = FALSE)
qotlog(p, shape)
rotlog(n, shape)


x, q

Vector of quantiles. For the density, it should be a vector with integer values > 1 in order for the probabilities to be positive.


vector of probabilities.


number of observations. Same as in runif.


The parameter value c described in in logff. Here it is called shape because 0<c<1 is the range.

log, log.p

Logical. If log.p = TRUE then all probabilities p are given as log(p).


The one-truncated logarithmic distribution is a logarithmic 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 logff.


dotlog gives the density, potlog gives the distribution function, qotlog gives the quantile function, and rotlog generates random deviates.


Given some response data, the VGAM family function otlog estimates the parameter shape. Function potlog() suffers from the problems that plog sometimes has.


T. W. Yee

See Also

Gaitdlog, otlog, rlog, Oilog.


dotlog(1:20, 0.5)
rotlog(20, 0.5)

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

VGAMdata documentation built on March 18, 2022, 8:03 p.m.