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

 Log R Documentation

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)`.

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

Examples

``````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")
## End(Not run)
``````

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.