distr6 (version 1.3.5)

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.

See Also

listDistributions for all available distributions.

Examples

# 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)

# }