VGAMdata (version 1.1-9)

Otlog: 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)


dotlog gives the density,

potlog gives the distribution function,

qotlog gives the quantile function, and

rotlog generates random deviates.


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).


T. W. Yee


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.

See Also

Gaitdlog, otlog, rlog, Oilog.


Run this code
dotlog(1:20, 0.5)
rotlog(20, 0.5)

if (FALSE)  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 distn: blue=PMF; orange=CDF")
lines(x+0.1, potlog(x, shape), col = "orange", lty = 3, type = "h") 

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