# 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`

- Keywords
- distribution

##### 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`

##### 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.
# }
```

*Documentation reproduced from package distr, version 2.8.0, License: LGPL-3*