# logUC: Logarithmic Distribution In VGAM: Vector Generalized Linear and Additive Models

## Description

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

## Usage

 ```1 2 3 4``` ```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)`.

## Details

The details are given in `logff`.

## Value

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

## Note

Given some response data, the VGAM family function `logff` estimates the parameter `shape`. 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).

T. W. Yee

## References

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

`logff`, `Gaitlog`, `Oilog`. `Otlog`.
 ```1 2 3 4 5 6 7 8 9``` ```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=density; orange=distribution function") lines(x + 0.1, plog(x, shape = shape), col = "orange", lty = 3, type = "h") ## End(Not run) ```