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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.
Returns an R6 object inheriting from class SDistribution.
Normal$new(mean = 0, var = 1, sd = NULL, prec = NULL, decorators = NULL, verbose = FALSE)
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.
The Normal distribution is parameterised with mean
as a numeric, and either var
, sd
or prec
as numerics. These are related via, prec
is given then sd
and var
are ignored. If sd
is given then var
is ignored.
Variable | Return |
name |
Name of distribution. |
short_name |
Id of distribution. |
description |
Brief description of distribution. |
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
The Normal distribution parameterised with variance,
The distribution is supported on the Reals.
Also known as the Gaussian distribution.
McLaughlin, M. P. (2001). A compendium of common probability distributions (pp. 2014-01). Michael P. McLaughlin.
listDistributions
for all available distributions.
# 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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