# 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.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### concept

- absolutely continuous distribution
- Log-Normal distribution
- S4 distribution class

##### 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.
```

*Documentation reproduced from package distr, version 2.3.1, License: LGPL-3*