Normal: Normal Distribution Class

Description

Mathematical and statistical functions for the Normal distribution, which is commonly used in significance testing, for representing models with a bell curve, and as a result of the central limit theorem.

Value

Returns an R6 object inheriting from class SDistribution.

Constructor

Normal$new(mean = 0, var = 1, sd = NULL, prec = NULL, decorators = NULL, verbose = FALSE)

Constructor Arguments

Argument	Type	Details
`mean`	numeric	mean, location parameter.
`var`	numeric	variance, squared scale parameter.
`sd`	numeric	standard deviation, scale parameter.
`prec`	numeric	precision, inverse squared scale parameter.

decorators Decorator decorators to add functionality. See details.

Constructor Details

The Normal distribution is parameterised with mean as a numeric, and either var, sd or prec as numerics. These are related via, $$sd = \sqrt(var)$$$$prec = 1/var$$ If prec is given then sd and var are ignored. If sd is given then var 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 Normal distribution parameterised with variance, $\sigma^2$, and mean, $\mu$, is defined by the pdf, $$f(x) = exp(-(x-\mu)^2/(2\sigma^2)) / \sqrt{2\pi\sigma^2}$$ for $\mu \epsilon R$ and $\sigma^2 > 0$.

The distribution is supported on the Reals.

Also known as the 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 {
# Different parameterisations
Normal$new(var = 1, mean = 1)
Normal$new(prec = 2, mean = 1)
Normal$new(mean = 1, sd = 2)

x <- Normal$new(verbose = TRUE) # Standard normal default

# Update parameters
x$setParameterValue(var = 2)
x$parameters()

# 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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