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.
Returns an R6 object inheriting from class SDistribution.
The distribution is supported on the Positive Reals.
Lnorm(meanlog = 0, varlog = 1)
N/A
Also known as the Log-Gaussian distribution.
distr6::Distribution -> distr6::SDistribution -> Lognormal
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.
new()Creates a new instance of this R6 class.
Lognormal$new( meanlog = NULL, varlog = NULL, sdlog = NULL, preclog = NULL, mean = NULL, var = NULL, sd = NULL, prec = NULL, decorators = NULL )
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.
Lognormal$new(var = 2, mean = 1) Lognormal$new(meanlog = 2, preclog = 5)
mean()The arithmetic mean of a (discrete) probability distribution X is the expectation $$E_X(X) = \sum p_X(x)*x$$ with an integration analogue for continuous distributions.
Lognormal$mean(...)
...Unused.
mode()The mode of a probability distribution is the point at which the pdf is a local maximum, a distribution can be unimodal (one maximum) or multimodal (several maxima).
Lognormal$mode(which = "all")
which(character(1) | numeric(1)
Ignored if distribution is unimodal. Otherwise "all" returns all modes, otherwise specifies
which mode to return.
...Unused.
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).
Lognormal$median()
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.
Lognormal$variance(...)
...Unused.
skewness()The skewness of a distribution is defined by the third standardised moment, $$sk_X = E_X[\frac{x - \mu}{\sigma}^3]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution.
Lognormal$skewness(...)
...Unused.
kurtosis()The kurtosis of a distribution is defined by the fourth standardised moment, $$k_X = E_X[\frac{x - \mu}{\sigma}^4]$$ where \(E_X\) is the expectation of distribution X, \(\mu\) is the mean of the distribution and \(\sigma\) is the standard deviation of the distribution. Excess Kurtosis is Kurtosis - 3.
Lognormal$kurtosis(excess = TRUE, ...)
excess(logical(1))
If TRUE (default) excess kurtosis returned.
...Unused.
entropy()The entropy of a (discrete) distribution is defined by $$- \sum (f_X)log(f_X)$$ where \(f_X\) is the pdf of distribution X, with an integration analogue for continuous distributions.
Lognormal$entropy(base = 2, ...)
base(integer(1))
Base of the entropy logarithm, default = 2 (Shannon entropy)
...Unused.
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.
Lognormal$mgf(t, ...)
t(integer(1))
t integer to evaluate function at.
...Unused.
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.
Lognormal$pgf(z, ...)
z(integer(1))
z integer to evaluate probability generating function at.
...Unused.
clone()The objects of this class are cloneable with this method.
Lognormal$clone(deep = FALSE)
deepWhether to make a deep clone.
The Log-Normal distribution parameterised with logmean, \(\mu\), and logvar, \(\sigma\), is defined by the pdf, $$exp(-(log(x)-\mu)^2/2\sigma^2)/(x\sigma\sqrt(2\pi))$$ for \(\mu \epsilon R\) and \(\sigma > 0\).
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
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
# NOT RUN {
## ------------------------------------------------
## Method `Lognormal$new`
## ------------------------------------------------
Lognormal$new(var = 2, mean = 1)
Lognormal$new(meanlog = 2, preclog = 5)
# }
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