VGAM (version 1.1-6)

# Log: Logarithmic Distribution

## Description

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

## Usage

```dlog(x, shape, log = FALSE)
plog(q, shape, lower.tail = TRUE, log.p = FALSE)
qlog(p, shape)
rlog(n, shape)```

## Arguments

x, q, p, n, lower.tail

Same interpretation as in `runif`.

shape

The shape parameter value \(c\) described in in `logff`.

log, log.p

Logical. If `log.p = TRUE` then all probabilities `p` are given as `log(p)`.

## Value

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

## Details

The details are given in `logff`.

## References

Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.

`logff`, `Gaitdlog`, `Oilog`. `Otlog`.

## Examples

Run this code
``````# NOT RUN {
dlog(1:20, 0.5)
rlog(20, 0.5)

# }
# NOT RUN {
shape <- 0.8; x <- 1:10
plot(x, dlog(x, shape = shape), type = "h", ylim = 0:1,
sub = "shape=0.8", las = 1, col = "blue", ylab = "shape",
main = "Logarithmic distribution: blue=PDF; orange=CDF")
lines(x + 0.1, plog(x, shape), col = "orange", lty = 3, type = "h")
# }
``````

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