cfS_Gaussian: Characteristic function of a GAUSSIAN (standard normal)...

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Characteristic function of a GAUSSIAN (standard normal) distribution

Description

cfS_Gaussian(t, mu, sigma, coef, niid) evaluates the characteristic function cf(t) of a GAUSSIAN (standard normal) distribution.

cfS_Gaussian is an ALIAS of the more general function cf_Normal, used to evaluate the characteristic function of a linear combination of independent normally distributed random variables.

The characteristic function of the standard normally distributed random variable, X ~ N(0,1), is defined by

cf(t) = cfS_Gaussian(t) = exp(-t^2/2).

Usage

cfS_Gaussian(t, mu, sigma, coef, niid)

Arguments

t	vector or array of real values, where the CF is evaluated.
mu	vector of mean values parameters.
sigma	vector of dispersion parameters.
coef	vector of coefficients of the linear combination of Normally distributed random variables. If coef is scalar, it is assumed that all coefficients are equal. If empty, default value is coef = 1.
niid	scalar convolution coeficient.

Value

Characteristic function cf(t) of a GAUSSIAN (standard normal) distribution.

Note

Ver.: 16-Sep-2018 19:08:06 (consistent with Matlab CharFunTool v1.3.0, 02-Jun-2017 12:08:24).

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Normal_distribution.

Other Continuous Probability Distribution: cfS_Arcsine(), cfS_Beta(), cfS_Laplace(), cfS_Rectangular(), cfS_Student(), cfS_TSP(), cfS_Trapezoidal(), cfS_Triangular(), cfS_Wigner(), cfX_ChiSquare(), cfX_Exponential(), cfX_FisherSnedecor(), cfX_Gamma(), cfX_InverseGamma(), cfX_LogNormal(), cf_ArcsineSymmetric(), cf_BetaNC(), cf_BetaSymmetric(), cf_Beta(), cf_ChiSquare(), cf_Exponential(), cf_FisherSnedecorNC(), cf_FisherSnedecor(), cf_Gamma(), cf_InverseGamma(), cf_Laplace(), cf_LogRV_BetaNC(), cf_LogRV_Beta(), cf_LogRV_ChiSquareNC(), cf_LogRV_ChiSquare(), cf_LogRV_FisherSnedecorNC(), cf_LogRV_FisherSnedecor(), cf_LogRV_MeansRatioW(), cf_LogRV_MeansRatio(), cf_LogRV_WilksLambdaNC(), cf_LogRV_WilksLambda(), cf_Normal(), cf_RectangularSymmetric(), cf_Student(), cf_TSPSymmetric(), cf_TrapezoidalSymmetric(), cf_TriangularSymmetric(), cf_vonMises()

Other Symmetric Probability Distribution: cfS_Arcsine(), cfS_Beta(), cfS_Laplace(), cfS_Rectangular(), cfS_Student(), cfS_Trapezoidal(), cf_ArcsineSymmetric(), cf_BetaSymmetric(), cf_RectangularSymmetric(), cf_TSPSymmetric(), cf_TrapezoidalSymmetric()

Examples

## EXAMPLE1
# CF of the Gaussian distribution N(0,1)
t <- seq(-5, 5, length.out = 501)
plotReIm(function(t)
        cfS_Gaussian(t), t, title = "CF of the Gaussian distribution N(0,1)")

## EXAMPLE2
# PDF/CDF of the Gaussian distribution N(0,1)
cf <- function(t)
        cfS_Gaussian(t)
x <- seq(-4, 4, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
options <- list()
options$N <- 2 ^ 5
options$SixSigmaRule <- 8
result <- cf2DistGP(cf, x, prob, options)

gajdosandrej/CharFunToolR documentation built on June 3, 2024, 7:46 p.m.