Lognormal: Log-Normal Distribution Class

Description Details Value Distribution support Default Parameterisation Omitted Methods Also known as Super classes Public fields Methods References See Also Examples

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)

Omitted Methods

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(...)
Arguments
...

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(...)
Arguments
...

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(...)
Arguments
...

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, NegativeBinomial, Normal, Pareto, Poisson, Rayleigh, ShiftedLoglogistic, StudentTNoncentral, StudentT, Triangular, Uniform, Wald, Weibull, WeightedDiscrete

Examples

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

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

distr6 documentation built on Sept. 6, 2021, 9:10 a.m.