R: One-truncated Logarithmic Distribution

Otlog {VGAM} | R Documentation

## 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)

### 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)`.

### 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`.

### Value

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

### Note

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

### Author(s)

T. W. Yee

### See Also

`Gaitlog`, `otlog`, `rlog`, `Oilog`.

### Examples

    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)

[Package VGAM version 1.1-3 Index]