Log {VGAM} | R Documentation

## Logarithmic Distribution

### Description

Density, distribution function, and random generation for the logarithmic distribution.

### Usage

    dlog(x, prob, log=FALSE)
    plog(q, prob, log.p=FALSE)
    rlog(n, prob, Smallno=1.0e-6)

### Arguments

`x, q` | Vector of quantiles. For the density, it should be a vector with positive integer values in order for the probabilities to be positive.
`n` | number of observations. A single positive integer.
`prob` | The parameter value c described in in `logff`. Here it is called `prob` because 0<c<1 is the range. For `rlog()` this parameter must be of length 1.
`log, log.p` | Logical. If `log.p=TRUE` then all probabilities `p` are given as `log(p)`.
`Smallno` | Numeric, a small value used by the rejection method for determining the upper limit of the distribution. That is, `plog(U, prob) > 1-Smallno` where `U` is the upper limit.

### Details

The details are given in `logff`.

### Value

`dlog` gives the density, `plog` gives the distribution function, and `rlog` generates random deviates.

### Note

Given some response data, the VGAM family function `logff` estimates the parameter `prob`. For `plog()`, if argument `q` contains large values and/or `q` is long in length then the memory requirements may be very high. Very large values in `q` are handled by an approximation by Owen (1965).

### Author(s)

T. W. Yee

### References

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

### See Also

`logff`.

### Examples

    dlog(1:20, 0.5)
    rlog(20, 0.5)

    ## Not run:
    prob = 0.8; x = 1:10
    plot(x, dlog(x, prob=prob), type="h", ylim=0:1,
         sub="prob=0.8", las=1, col="blue", ylab="Probability",
         main="Logarithmic distribution: blue=density; red=distribution function")
    lines(x+0.1, plog(x, prob=prob), col="red", lty=3, type="h")
    ## End(Not run)

[Package VGAM version 0.7-9 Index]