| Lnorm-class {distr} | R Documentation |
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.
img:"Reals": The space of the image of this distribution has got dimension 1
and the name "Real Space". param:"LnormParameter": the parameter of this distribution (meanlog and sdlog),
declared at its instantiation r:"function": generates random numbers (calls function rlnorm)d:"function": density function (calls function dlnorm)p:"function": cumulative function (calls function plnorm)q:"function": inverse of the cumulative function (calls function qlnorm)
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 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-bayreuth.de,
Matthias Kohl Matthias.Kohl@stamats.de
LnormParameter-class
AbscontDistribution-class
Reals-class
rlnorm
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.