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Lambert W specifications


Unique identifier OMICS_26447
Name Lambert W
Alternative name LambertW
Software type Package/Module
Interface Command line interface
Restrictions to use None
Operating system Unix/Linux, Mac OS, Windows
Programming languages R
License GNU General Public License version 2.0
Computer skills Advanced
Version 0.6.4
Stability Stable
stats, RColorBrewer, graphics, testthat, grDevices, Rcpp, ggplot2, MASS, Rsolnp, reshape2, moments, boot, numDeriv, lamW(≥1.0.0), nortest
Source code URL
Maintained Yes




No version available



  • person_outline Sun Yi
  • person_outline Georg Goerg

Publication for Lambert W

Lambert W citations


Hyper Transcranial Alternating Current Stimulation: Experimental Manipulation of Inter Brain Synchrony

Front Hum Neurosci
PMCID: 5682643
PMID: 29167638
DOI: 10.3389/fnhum.2017.00539
call_split See protocol

[…] rony sum scores were calculated for each trial. To approximate a normal distribution outliers were removed (>2.5 standard deviation) and asynchrony scores were Lambert-transformed using R () and the ‘LambertW’ package (). Preferred drumming tempo was measured as mean inter-response interval in ms for each trial and also Lambert-transformed to approximate a normal distribution. The Lambert-transfor […]


Experimental and theoretical study of magnetohydrodynamic ship models

PLoS One
PMCID: 5493298
PMID: 28665941
DOI: 10.1371/journal.pone.0178599

[…] (), and taking fringing effect into account, it leads to U0=δU+U=E0+A0lnI+RI+kudBH,(13) where R=ri+r*=ri+H/(σlx*lz) and lx* is given by . Note that can be solved for the current, leading to lnI=VA0-LambertW(RA0eV/A0),(14) with LambertW the Lambert W function and the voltage V = U0 − E0 − kudBH, where V > 0 for a propulsive thruster.For very large currents, the rate of electrolysis driven reactio […]


Denaturation of proteins by surfactants studied by the Taylor dispersion analysis

PLoS One
PMCID: 5398553
PMID: 28426809
DOI: 10.1371/journal.pone.0175838

[…] ary radius, r is the external radius of curvature of the coiled capillary, A = 0.87 ± 0.02 and B = -3.8 ± 0.2 are fitted parameters. The formula 3.2.1 can be simplified by replacement of the function LambertW (-1,x) with its asymptotic expansion: Lambert W ( −1,x)≈W(x)=L1−L2+L2L1+L2(−2+L2)2L12(2)Where: L1 = ln(-x) and L2 = ln (-ln (-x)).Here, we apply modified Taylor dispersion method which is mor […]


A theoretical model of the relationship between the h index and other simple citation indicators

PMCID: 5438441
PMID: 28596626
DOI: 10.1007/s11192-017-2351-9

[…] tisfying y=WyeWy, and can be currently computed using mathematical software, for example the Mathematica® 10.0 software package (Wolfram Research, Inc. ; it is implemented in the Wolfram Language as “LambertW”), or also using the R statistical computing environment (R Development Core Team ).Hence7-hlogm1+m=W-Tlogm1+m,that is, equivalently,8hW0=WTlog1+m-1log1+m-1,where we have adopted a new symbol […]


An explicit solution for calculating optimum spawning stock size from Ricker’s stock recruitment model

PMCID: 4800783
PMID: 27004147
DOI: 10.7717/peerj.1623

[…] results from my R implementation for a range of a and b in . For those preferring to use Microsoft Excel, there is no built-in function to calculate W(x), but I have implemented as the VBA function ‘LAMBERTW’ in the Microsoft Excel add-in file ‘LambertWfunc.xlam’ (see for download and install instructions).Here I have outlined a new method to easily calculate SMSY from the productivity (a) and d […]


The Lambert Way to Gaussianize Heavy Tailed Data with the Inverse of Tukey's h Transformation as a Special Case

Sci World J
PMCID: 4562338
PMID: 26380372
DOI: 10.1155/2015/909231

[…] ailed derivations and proofs are given in the Supplementary Material available online at, figures, and simulations were done in R []. The R package  LambertW implements most of the presented methodology and is publicly available on CRAN. […]


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Lambert W institution(s)
Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA
Lambert W funding source(s)
Supported by NSF Grant #0555765 and in part by a Career Award at the Scientific Interface from the Burroughs Welcome Fund.

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