# R/SDistribution_Normal.R In distr6: The Complete R6 Probability Distributions Interface

# nolint start
#' @name Normal
#' @template SDist
#' @templateVar ClassName Normal
#' @templateVar DistName Normal
#' @templateVar uses in significance testing, for representing models with a bell curve, and as a result of the central limit theorem
#' @templateVar params variance, \eqn{\sigma^2}, and mean, \eqn{\mu},
#' @templateVar pdfpmf pdf
#' @templateVar pdfpmfeq \deqn{f(x) = exp(-(x-\mu)^2/(2\sigma^2)) / \sqrt{2\pi\sigma^2}}
#' @templateVar paramsupport \eqn{\mu \epsilon R} and \eqn{\sigma^2 > 0}
#' @templateVar distsupport the Reals
#' @templateVar default mean = 0, var = 1
#' @templateVar aka Gaussian
#' @aliases Gaussian
# nolint end
#' @template class_distribution
#' @template method_mode
#' @template method_entropy
#' @template method_kurtosis
#' @template method_pgf
#' @template method_mgfcf
#' @template param_decorators
#' @template field_packages
#'
#' @family continuous distributions
#' @family univariate distributions
#'
#' @export
Normal <- R6Class("Normal",
inherit = SDistribution, lock_objects = F,
public = list(
# Public fields
name = "Normal",
short_name = "Norm",
description = "Normal Probability Distribution.",
packages = "stats",

# Public methods
# initialize

#' @description
#' Creates a new instance of this [R6][R6::R6Class] class.
#' @param mean (numeric(1))\cr
#' Mean of the distribution, defined on the Reals.
#' @param var (numeric(1))\cr
#' Variance of the distribution, defined on the positive Reals.
#' @param sd (numeric(1))\cr
#' Standard deviation of the distribution, defined on the positive Reals. sd = sqrt(var).
#' If provided then var ignored.
#' @param prec (numeric(1))\cr
#' Precision of the distribution, defined on the positive Reals. prec = 1/var.
#' If provided then var ignored.
initialize = function(mean = NULL, var = NULL, sd = NULL, prec = NULL,
decorators = NULL) {
super$initialize( decorators = decorators, support = Reals$new(),
symmetry = "sym",
type = Reals$new() ) }, # stats #' @description #' The arithmetic mean of a (discrete) probability distribution X is the expectation #' \deqn{E_X(X) = \sum p_X(x)*x} #' with an integration analogue for continuous distributions. #' @param ... Unused. mean = function(...) { unlist(self$getParameterValue("mean"))
},

#' @description
#' The mode of a probability distribution is the point at which the pdf is
#' a local maximum, a distribution can be unimodal (one maximum) or multimodal (several
#' maxima).
mode = function(which = "all") {
unlist(self$getParameterValue("mean")) }, #' @description #' The variance of a distribution is defined by the formula #' \deqn{var_X = E[X^2] - E[X]^2} #' where \eqn{E_X} is the expectation of distribution X. If the distribution is multivariate the #' covariance matrix is returned. #' @param ... Unused. variance = function(...) { unlist(self$getParameterValue("var"))
},

#' @description
#' The skewness of a distribution is defined by the third standardised moment,
#' \deqn{sk_X = E_X[\frac{x - \mu}{\sigma}^3]}{sk_X = E_X[((x - \mu)/\sigma)^3]}
#' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the
#' distribution and \eqn{\sigma} is the standard deviation of the distribution.
#' @param ... Unused.
skewness = function(...) {
numeric(length(self$getParameterValue("var"))) }, #' @description #' The kurtosis of a distribution is defined by the fourth standardised moment, #' \deqn{k_X = E_X[\frac{x - \mu}{\sigma}^4]}{k_X = E_X[((x - \mu)/\sigma)^4]} #' where \eqn{E_X} is the expectation of distribution X, \eqn{\mu} is the mean of the #' distribution and \eqn{\sigma} is the standard deviation of the distribution. #' Excess Kurtosis is Kurtosis - 3. #' @param ... Unused. kurtosis = function(excess = TRUE, ...) { if (excess) { return(numeric(length(self$getParameterValue("var"))))
} else {
return(numeric(length(self$getParameterValue("var"))) + 3) } }, #' @description #' The entropy of a (discrete) distribution is defined by #' \deqn{- \sum (f_X)log(f_X)} #' where \eqn{f_X} is the pdf of distribution X, with an integration analogue for #' continuous distributions. #' @param ... Unused. entropy = function(base = 2, ...) { 0.5 * log(2 * pi * exp(1) * unlist(self$getParameterValue("var")), base)
},

#' @description The moment generating function is defined by
#' \deqn{mgf_X(t) = E_X[exp(xt)]}
#' where X is the distribution and \eqn{E_X} is the expectation of the distribution X.
#' @param ... Unused.
mgf = function(t, ...) {
return(exp((self$getParameterValue("mean") * t) + (self$getParameterValue("var") * t^2 * 0.5)))
},

#' @description The characteristic function is defined by
#' \deqn{cf_X(t) = E_X[exp(xti)]}
#' where X is the distribution and \eqn{E_X} is the expectation of the distribution X.
#' @param ... Unused.
cf = function(t, ...) {
return(exp((1i * self$getParameterValue("mean") * t) - (self$getParameterValue("var") * t^2 * 0.5)))
},

#' @description The probability generating function is defined by
#' \deqn{pgf_X(z) = E_X[exp(z^x)]}
#' where X is the distribution and \eqn{E_X} is the expectation of the distribution X.
#' @param ... Unused.
pgf = function(z, ...) {
return(NaN)
}
),

private = list(
# dpqr
.pdf = function(x, log = FALSE) {
mean <- self$getParameterValue("mean") sd <- self$getParameterValue("sd")
call_C_base_pdqr(
fun = "dnorm",
x = x,
args = list(
mean = unlist(mean),
sd = unlist(sd)
),
log = log,
vec = test_list(mean)
)
},
.cdf = function(x, lower.tail = TRUE, log.p = FALSE) {
mean <- self$getParameterValue("mean") sd <- self$getParameterValue("sd")
call_C_base_pdqr(
fun = "pnorm",
x = x,
args = list(
mean = unlist(mean),
sd = unlist(sd)
),
lower.tail = lower.tail,
log = log.p,
vec = test_list(mean)
)
},
.quantile = function(p, lower.tail = TRUE, log.p = FALSE) {
mean <- self$getParameterValue("mean") sd <- self$getParameterValue("sd")
call_C_base_pdqr(
fun = "qnorm",
x = p,
args = list(
mean = unlist(mean),
sd = unlist(sd)
),
lower.tail = lower.tail,
log = log.p,
vec = test_list(mean)
)
},
.rand = function(n) {
mean <- self$getParameterValue("mean") sd <- self$getParameterValue("sd")
call_C_base_pdqr(
fun = "rnorm",
x = n,
args = list(
mean = unlist(mean),
sd = unlist(sd)
),
vec = test_list(mean)
)
},

# traits
.traits = list(valueSupport = "continuous", variateForm = "univariate")
)
)

.distr6$distributions <- rbind( .distr6$distributions,
data.table(
ShortName = "Norm", ClassName = "Normal",
Type = "\u211D", ValueSupport = "continuous",
VariateForm = "univariate",
Package = "stats", Tags = "locscale"
)
)


## Try the distr6 package in your browser

Any scripts or data that you put into this service are public.

distr6 documentation built on March 28, 2022, 1:05 a.m.