# 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

`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.

### 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@uni-oldenburg.de,

Matthias Kohl Matthias.Kohl@stamats.de

### See Also

`LnormParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rlnorm`

### Examples

1 2 3 4 5 6 7 | ```
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.
``` |