Class "Lnorm"
The log normal distribution has density
d(x) = 1/(sqrt(2 pi) sigma x) e^-((log x - mu)^2 / (2 sigma^2))
where μ, by default =0, and σ, by default =1, are the mean and standard
deviation of the logarithm.
C.f. rlnorm
Objects can be created by calls of the form Lnorm(meanlog, sdlog).
This object is a log normal distribution.
imgObject of class "Reals": The space of the image of this distribution has got dimension 1
and the name "Real Space".
paramObject of class "LnormParameter": the parameter of this distribution (meanlog and sdlog),
declared at its instantiation
rObject of class "function": generates random numbers (calls function rlnorm)
dObject of class "function": density function (calls function dlnorm)
pObject of class "function": cumulative function (calls function plnorm)
qObject of class "function": inverse of the cumulative function (calls function qlnorm)
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject of class "DistributionSymmetry";
used internally to avoid unnecessary calculations.
Class "AbscontDistribution", directly.
Class "UnivariateDistribution", by class "AbscontDistribution".
Class "Distribution", by class "AbscontDistribution".
signature(.Object = "Lnorm"): initialize method
signature(object = "Lnorm"): returns the slot meanlog of the parameter of the distribution
signature(object = "Lnorm"): modifies the slot meanlog of the parameter of the distribution
signature(object = "Lnorm"): returns the slot sdlog of the parameter of the distribution
signature(object = "Lnorm"): modifies the slot sdlog of the parameter of the distribution
signature(e1 = "Lnorm", e2 = "numeric"):
For the Lognormal distribution we use its closedness under positive scaling transformations.
The mean is E(X) = exp(μ + 1/2 σ^2), and the variance Var(X) = exp(2*mu + sigma^2)*(exp(sigma^2) - 1) and hence the coefficient of variation is sqrt(exp(sigma^2) - 1) which is approximately σ when that is small (e.g., σ < 1/2).
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de,
Matthias Kohl Matthias.Kohl@stamats.de
L <- Lnorm(meanlog=1,sdlog=1) # L is a lnorm distribution with mean=1 and sd=1. r(L)(1) # one random number generated from this distribution, e.g. 3.608011 d(L)(1) # Density of this distribution is 0.2419707 for x=1. p(L)(1) # Probability that x<1 is 0.1586553. q(L)(.1) # Probability that x<0.754612 is 0.1. ## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.) meanlog(L) # meanlog of this distribution is 1. meanlog(L) <- 2 # meanlog of this distribution is now 2.
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