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)
Omitted Methods
N/A
Also known as
Also known as the Log-Gaussian distribution.
Super classes
distr6::Distribution -> distr6::SDistribution -> Lognormal
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages 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$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01).
Michael P. McLaughlin.
See Also
Other continuous distributions:
Arcsine,
BetaNoncentral,
Beta,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Dirichlet,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
MultivariateNormal,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other univariate distributions:
Arcsine,
Bernoulli,
BetaNoncentral,
Beta,
Binomial,
Categorical,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Degenerate,
DiscreteUniform,
Empirical,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Geometric,
Gompertz,
Gumbel,
Hypergeometric,
InverseGamma,
Laplace,
Logarithmic,
Logistic,
Loglogistic,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
Examples
## ------------------------------------------------
## Method `Lognormal$new`
## ------------------------------------------------
Lognormal$new(var = 2, mean = 1)
Lognormal$new(meanlog = 2, preclog = 5)
distr6 documentation built on March 28, 2022, 1:05 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
| 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)
Omitted Methods
N/A
Also known as
Also known as the Log-Gaussian distribution.
Super classes
distr6::Distribution -> distr6::SDistribution -> Lognormal
Public fields
nameFull name of distribution.
short_nameShort name of distribution for printing.
descriptionBrief description of the distribution.
packagesPackages 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$new( meanlog = NULL, varlog = NULL, sdlog = NULL, preclog = NULL, mean = NULL, var = NULL, sd = NULL, prec = NULL, decorators = NULL )
Arguments
meanlog(numeric(1))
Mean of the distribution on the log scale, defined on the Reals.varlog(numeric(1))
Variance of the distribution on the log scale, defined on the positive Reals.sdlog(numeric(1))
Standard deviation of the distribution on the log scale, defined on the positive Reals.sdlog = varlog^2
. If
preclogmissing andsdloggiven then all other parameters exceptmeanlogare ignored.preclog(numeric(1))
Precision of the distribution on the log scale, defined on the positive Reals.preclog = 1/varlog
. If given then all other parameters except
meanlogare ignored.mean(numeric(1))
Mean of the distribution on the natural scale, defined on the positive Reals.var(numeric(1))
Variance of the distribution on the natural scale, defined on the positive Reals.var = (exp(var) - 1)) * exp(2 * meanlog + varlog)
sd(numeric(1))
Standard deviation of the distribution on the natural scale, defined on the positive Reals.sd = var^2
. If
precmissing andsdgiven then all other parameters exceptmeanare ignored.prec(numeric(1))
Precision of the distribution on the natural scale, defined on the Reals.prec = 1/var
. If given then all other parameters except
meanare ignored.decorators(character())
Decorators to add to the distribution during construction.
Examples
Lognormal$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$kurtosis(excess = TRUE, ...)
Arguments
excess(logical(1))
IfTRUE(default) excess kurtosis returned....Unused.
Method entropy()
The entropy of a (discrete) distribution is defined by
- ∑ (f_X)log(f_X)
where f_X is the pdf of distribution X, with an integration analogue for continuous distributions.
Usage
Lognormal$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$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
References
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
See Also
Other continuous distributions:
Arcsine,
BetaNoncentral,
Beta,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Dirichlet,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Gompertz,
Gumbel,
InverseGamma,
Laplace,
Logistic,
Loglogistic,
MultivariateNormal,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull
Other univariate distributions:
Arcsine,
Bernoulli,
BetaNoncentral,
Beta,
Binomial,
Categorical,
Cauchy,
ChiSquaredNoncentral,
ChiSquared,
Degenerate,
DiscreteUniform,
Empirical,
Erlang,
Exponential,
FDistributionNoncentral,
FDistribution,
Frechet,
Gamma,
Geometric,
Gompertz,
Gumbel,
Hypergeometric,
InverseGamma,
Laplace,
Logarithmic,
Logistic,
Loglogistic,
Matdist,
NegativeBinomial,
Normal,
Pareto,
Poisson,
Rayleigh,
ShiftedLoglogistic,
StudentTNoncentral,
StudentT,
Triangular,
Uniform,
Wald,
Weibull,
WeightedDiscrete
Examples
## ------------------------------------------------ ## Method `Lognormal$new` ## ------------------------------------------------ Lognormal$new(var = 2, mean = 1) Lognormal$new(meanlog = 2, preclog = 5)
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.