Lnorm-class {distr}R Documentation

Class "Lnorm"

Description

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 from the Class

Objects can be created by calls of the form Lnorm(meanlog, sdlog). This object is a log normal distribution.

Slots

img:
Object of class "Reals": The space of the image of this distribution has got dimension 1 and the name "Real Space".
param:
Object of class "LnormParameter": the parameter of this distribution (meanlog and sdlog), declared at its instantiation
r:
Object of class "function": generates random numbers (calls function rlnorm)
d:
Object of class "function": density function (calls function dlnorm)
p:
Object of class "function": cumulative function (calls function plnorm)
q:
Object of class "function": inverse of the cumulative function (calls function qlnorm)
.withArith:
logical: used internally to issue warnings as to interpretation of arithmetics
.withSim:
logical: used internally to issue warnings as to accuracy
.logExact:
logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExact:
logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

Extends

Class "AbscontDistribution", directly.
Class "UnivariateDistribution", by class "AbscontDistribution".
Class "Distribution", by class "AbscontDistribution".

Methods

initialize
signature(.Object = "Lnorm"): initialize method
meanlog
signature(object = "Lnorm"): returns the slot meanlog of the parameter of the distribution
meanlog<-
signature(object = "Lnorm"): modifies the slot meanlog of the parameter of the distribution
sdlog
signature(object = "Lnorm"): returns the slot sdlog of the parameter of the distribution
sdlog<-
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.

Note

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).

Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de

See Also

LnormParameter-class AbscontDistribution-class Reals-class rlnorm

Examples

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.
meanlog(L) # meanlog of this distribution is 1.
meanlog(L) <- 2 # meanlog of this distribution is now 2.

[Package distr version 2.1.1 Index]