logUC: Logarithmic Distribution

LogR Documentation

Logarithmic Distribution


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


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


x, q, p, n, lower.tail

Same interpretation as in runif.


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).


The details are given in logff.


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


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


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

See Also

logff, Gaitdlog, Oilog. Otlog.


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.