# glog

0th

Percentile

##### Compute Generalized Logarithm

The functions compute the generalized logarithm, which is more or less identical to the area hyperbolic sine, and their inverse; see details.

Keywords
univar
##### Usage
glog(x, base = exp(1))
glog10(x)
glog2(x)
inv.glog(x, base = exp(1))
inv.glog10(x)
inv.glog2(x)
##### Arguments
x

a numeric or complex vector.

base

a positive or a positive or complex number: the base with respect to which logarithms are computed. Defaults to e=exp(1).

##### Details

The function computes $$\log(x + \sqrt{x^2 + 1}) - \log(2)$$ where the first part corresponds to the area hyperbolic sine. Subtracting log(2) makes the function asymptotically identical to the logarithm.

##### Value

A vector of the same length as x containing the transformed values.

• glog
• glog10
• glog2
• inv.glog
• inv.glog10
• inv.glog2
##### Examples
# NOT RUN {
curve(log, from = -3, to = 5)
curve(glog, from = -3, to = 5, add = TRUE, col = "orange")
legend("topleft", fill = c("black", "orange"), legend = c("log", "glog"))

curve(log10(x), from = -3, to = 5)
curve(glog10(x), from = -3, to = 5, add = TRUE, col = "orange")
legend("topleft", fill = c("black", "orange"), legend = c("log10", "glog10"))

inv.glog(glog(10))
inv.glog(glog(10, base = 3), base = 3)
inv.glog10(glog10(10))
inv.glog2(glog2(10))
# }

Documentation reproduced from package MKdescr, version 0.4, License: LGPL-3

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