VGAMdata (version 1.1-9)

Otlog: One-truncated Logarithmic Distribution

Description

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

Usage

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

Value

dotlog gives the density,

potlog gives the distribution function,

qotlog gives the quantile function, and

rotlog generates random deviates.

Arguments

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.

p

vector of probabilities.

n

number of observations. Same as in runif.

shape

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).

Author

T. W. Yee

Details

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.

Examples

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")