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.

Examples

Run this code

# 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)

# }

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