logUC: Logarithmic Distribution

In VGAM: Vector Generalized Linear and Additive Models

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).

Author(s)

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.

See Also

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. 18, 2024, 9:09 a.m.