distr6 (version 1.3.6)

Lognormal: 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.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Lognormal$new(meanlog = 0, varlog = 1, sdlog = NULL, preclog = NULL, mean = 1, var = NULL, sd = NULL, prec = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
meanlog	numeric	mean of the distribution on the log scale.
varlog	numeric	variance of the distribution on the log scale.
sdlog	numeric	standard deviation of the distribution on the log scale.
preclog	numeric	precision of the distribution on the log scale.
mean	numeric	mean of the distribution on the natural scale.
var	numeric	variance of the distribution on the natural scale.
sd	numeric	standard deviation of the distribution on the natural scale.
prec	numeric	precision of the distribution on the natural scale.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Log-Normal distribution is parameterised with either meanlog and varlog, sdlog or preclog, or mean and var, sd or prec. These are related via $$var = (exp(var) - 1)) * exp(2 * meanlog + varlog)$$ $$sdlog = varlog^2$$ $$sd = var^2$$ Analogously for prec and preclog. If prec is given then all other parameters other than mean are ignored. If sd is given then all other parameters (except prec) are ignored. If var is given then all log parameters are ignored. If preclog is given then varlog and sdlog are ignored. Finally if sdlog is given then varlog is ignored.

Public Variables

Variable	Return
name	Name of distribution.
short_name	Id of distribution.
description	Brief description of distribution.

Public Methods

Accessor Methods	Link
decorators	decorators
traits	traits
valueSupport	valueSupport
variateForm	variateForm
type	type
properties	properties
support	support
symmetry	symmetry
sup	sup
inf	inf
dmax	dmax
dmin	dmin
skewnessType	skewnessType
kurtosisType	kurtosisType

Statistical Methods Link pdf(x1, ..., log = FALSE, simplify = TRUE) pdf cdf(x1, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) cdf quantile(p, ..., lower.tail = TRUE, log.p = FALSE, simplify = TRUE) quantile.Distribution rand(n, simplify = TRUE) rand mean() mean.Distribution variance() variance stdev() stdev prec() prec cor() cor skewness() skewness kurtosis(excess = TRUE) kurtosis entropy(base = 2) entropy mgf(t) mgf cf(t) cf pgf(z) pgf median() median.Distribution iqr() iqr mode(which = "all") mode

Parameter Methods Link parameters(id) parameters getParameterValue(id, error = "warn") getParameterValue setParameterValue(..., lst = NULL, error = "warn") setParameterValue

Validation Methods Link liesInSupport(x, all = TRUE, bound = FALSE) liesInSupport liesInType(x, all = TRUE, bound = FALSE) liesInType

Representation Methods Link strprint(n = 2) strprint print(n = 2) print summary(full = T) summary.Distribution

Details

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 \(\sigma > 0\).

The distribution is supported on the Positive Reals.

cf is omitted as no closed form analytic expression could be found, decorate with CoreStatistics for numerical results.

Also known as the Log-Gaussian distribution.

References

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

See Also

listDistributions for all available distributions. Normal for the Normal distribution. CoreStatistics for numerical results.

Examples

# NOT RUN {
# Many parameterisations are possible
Lognormal$new(var = 2, mean = 1)
Lognormal$new(meanlog = 2, preclog = 5)
# Note parameters must be on same scale (log or natural)
Lognormal$new(meanlog = 4, sd = 2)

x <- Lognormal$new(verbose = TRUE) # meanlog = 0, sdlog = 1 default

# Update parameters
# When any parameter is updated, all others are too!
x$setParameterValue(meanlog = 3)
x$parameters()

# But you can only set parameters on the same scale, the below has no effect
x$setParameterValue(sd = 3)
# But this does
x$setParameterValue(sdlog = 3)

# d/p/q/r
x$pdf(5)
x$cdf(5)
x$quantile(0.42)
x$rand(4)

# Statistics
x$mean()
x$variance()

summary(x)

# }