# Lognormal: Log-Normal Distribution Class In distr6: The Complete R6 Probability Distributions Interface

 Lognormal R Documentation

## Log-Normal Distribution Class

### Description

Mathematical and statistical functions for the Log-Normal distribution, which is commonly used to model many natural phenomena as a result of growth driven by small percentage changes.

### Details

The Log-Normal distribution parameterised with logmean, μ, and logvar, σ, is defined by the pdf,

exp(-(log(x)-μ)^2/2σ^2)/(xσ√(2π))

for μ ε R and σ > 0.

### Value

Returns an R6 object inheriting from class SDistribution.

### Distribution support

The distribution is supported on the Positive Reals.

### Default Parameterisation

Lnorm(meanlog = 0, varlog = 1)

N/A

### Also known as

Also known as the Log-Gaussian distribution.

### Super classes

`distr6::Distribution` -> `distr6::SDistribution` -> `Lognormal`

### Public fields

`name`

Full name of distribution.

`short_name`

Short name of distribution for printing.

`description`

Brief description of the distribution.

`packages`

Packages required to be installed in order to construct the distribution.

### Methods

#### Public methods

Inherited methods

#### Method `new()`

Creates a new instance of this R6 class.

##### Usage
```Lognormal\$new(
meanlog = NULL,
varlog = NULL,
sdlog = NULL,
preclog = NULL,
mean = NULL,
var = NULL,
sd = NULL,
prec = NULL,
decorators = NULL
)```
##### Arguments
`meanlog`

`(numeric(1))`
Mean of the distribution on the log scale, defined on the Reals.

`varlog`

`(numeric(1))`
Variance of the distribution on the log scale, defined on the positive Reals.

`sdlog`

`(numeric(1))`
Standard deviation of the distribution on the log scale, defined on the positive Reals.

sdlog = varlog^2

. If `preclog` missing and `sdlog` given then all other parameters except `meanlog` are ignored.

`preclog`

`(numeric(1))`
Precision of the distribution on the log scale, defined on the positive Reals.

preclog = 1/varlog

. If given then all other parameters except `meanlog` are ignored.

`mean`

`(numeric(1))`
Mean of the distribution on the natural scale, defined on the positive Reals.

`var`

`(numeric(1))`
Variance of the distribution on the natural scale, defined on the positive Reals.

var = (exp(var) - 1)) * exp(2 * meanlog + varlog)

`sd`

`(numeric(1))`
Standard deviation of the distribution on the natural scale, defined on the positive Reals.

sd = var^2

. If `prec` missing and `sd` given then all other parameters except `mean` are ignored.

`prec`

`(numeric(1))`
Precision of the distribution on the natural scale, defined on the Reals.

prec = 1/var

. If given then all other parameters except `mean` are ignored.

`decorators`

`(character())`
Decorators to add to the distribution during construction.

##### Examples
```Lognormal\$new(var = 2, mean = 1)
Lognormal\$new(meanlog = 2, preclog = 5)
```

#### Method `mean()`

The arithmetic mean of a (discrete) probability distribution X is the expectation

E_X(X) = ∑ p_X(x)*x

with an integration analogue for continuous distributions.

##### Usage
`Lognormal\$mean(...)`
`...`

Unused.

#### Method `mode()`

The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).

##### Usage
`Lognormal\$mode(which = "all")`
##### Arguments
`which`

`(character(1) | numeric(1)`
Ignored if distribution is unimodal. Otherwise `"all"` returns all modes, otherwise specifies which mode to return.

`...`

Unused.

#### Method `median()`

Returns the median of the distribution. If an analytical expression is available returns distribution median, otherwise if symmetric returns `self\$mean`, otherwise returns `self\$quantile(0.5)`.

##### Usage
`Lognormal\$median()`

#### Method `variance()`

The variance of a distribution is defined by the formula

var_X = E[X^2] - E[X]^2

where E_X is the expectation of distribution X. If the distribution is multivariate the covariance matrix is returned.

##### Usage
`Lognormal\$variance(...)`
`...`

Unused.

#### Method `skewness()`

The skewness of a distribution is defined by the third standardised moment,

sk_X = E_X[((x - μ)/σ)^3]

where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution.

##### Usage
`Lognormal\$skewness(...)`
`...`

Unused.

#### Method `kurtosis()`

The kurtosis of a distribution is defined by the fourth standardised moment,

k_X = E_X[((x - μ)/σ)^4]

where E_X is the expectation of distribution X, μ is the mean of the distribution and σ is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.

##### Usage
`Lognormal\$kurtosis(excess = TRUE, ...)`
##### Arguments
`excess`

`(logical(1))`
If `TRUE` (default) excess kurtosis returned.

`...`

Unused.

#### Method `entropy()`

The entropy of a (discrete) distribution is defined by

- ∑ (f_X)log(f_X)

where f_X is the pdf of distribution X, with an integration analogue for continuous distributions.

##### Usage
`Lognormal\$entropy(base = 2, ...)`
##### Arguments
`base`

`(integer(1))`
Base of the entropy logarithm, default = 2 (Shannon entropy)

`...`

Unused.

#### Method `mgf()`

The moment generating function is defined by

mgf_X(t) = E_X[exp(xt)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
`Lognormal\$mgf(t, ...)`
##### Arguments
`t`

`(integer(1))`
t integer to evaluate function at.

`...`

Unused.

#### Method `pgf()`

The probability generating function is defined by

pgf_X(z) = E_X[exp(z^x)]

where X is the distribution and E_X is the expectation of the distribution X.

##### Usage
`Lognormal\$pgf(z, ...)`
##### Arguments
`z`

`(integer(1))`
z integer to evaluate probability generating function at.

`...`

Unused.

#### Method `clone()`

The objects of this class are cloneable with this method.

##### Usage
`Lognormal\$clone(deep = FALSE)`
##### Arguments
`deep`

Whether to make a deep clone.

### References

McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.

### See Also

Other continuous distributions: `Arcsine`, `BetaNoncentral`, `Beta`, `Cauchy`, `ChiSquaredNoncentral`, `ChiSquared`, `Dirichlet`, `Erlang`, `Exponential`, `FDistributionNoncentral`, `FDistribution`, `Frechet`, `Gamma`, `Gompertz`, `Gumbel`, `InverseGamma`, `Laplace`, `Logistic`, `Loglogistic`, `MultivariateNormal`, `Normal`, `Pareto`, `Poisson`, `Rayleigh`, `ShiftedLoglogistic`, `StudentTNoncentral`, `StudentT`, `Triangular`, `Uniform`, `Wald`, `Weibull`

Other univariate distributions: `Arcsine`, `Bernoulli`, `BetaNoncentral`, `Beta`, `Binomial`, `Categorical`, `Cauchy`, `ChiSquaredNoncentral`, `ChiSquared`, `Degenerate`, `DiscreteUniform`, `Empirical`, `Erlang`, `Exponential`, `FDistributionNoncentral`, `FDistribution`, `Frechet`, `Gamma`, `Geometric`, `Gompertz`, `Gumbel`, `Hypergeometric`, `InverseGamma`, `Laplace`, `Logarithmic`, `Logistic`, `Loglogistic`, `Matdist`, `NegativeBinomial`, `Normal`, `Pareto`, `Poisson`, `Rayleigh`, `ShiftedLoglogistic`, `StudentTNoncentral`, `StudentT`, `Triangular`, `Uniform`, `Wald`, `Weibull`, `WeightedDiscrete`

### Examples

```
## ------------------------------------------------
## Method `Lognormal\$new`
## ------------------------------------------------

Lognormal\$new(var = 2, mean = 1)
Lognormal\$new(meanlog = 2, preclog = 5)
```

distr6 documentation built on March 28, 2022, 1:05 a.m.