# 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

```
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 2.6, License: LGPL-3*