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)`.

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

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")
``````

Run the code above in your browser using DataLab