Lnorm-class

Class "Lnorm"

The log normal distribution has density $$ d(x) = \frac{1}{\sqrt{2\pi}\sigma x} e^{-(\log(x) - \mu)^2/2 \sigma^2}% $$ where \(\mu\), by default \(=0\), and \(\sigma\), by default \(=1\), are the mean and standard deviation of the logarithm. C.f. rlnorm

Note

The mean is \(E(X) = exp(\mu + 1/2 \sigma^2)\), 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 \(\sigma\) when that is small (e.g., \(\sigma < 1/2\)).

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

Symmetry

object of class "DistributionSymmetry"; used internally to avoid unnecessary calculations.

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.

See Also

LnormParameter-class AbscontDistribution-class Reals-class rlnorm

Aliases

• Lnorm-class
• Lnorm
• initialize,Lnorm-method

Examples

# NOT RUN {
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.
# }