cfS_Rectangular: Characteristic function of the zero-mean symmetric...

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

Characteristic function of the zero-mean symmetric RECTANGULAR distribution

Description

cfS_Rectangular(t, coef, niid) evaluates the characteristic function cf(t) of the zero-mean symmetric RECTANGULAR distribution defined on the interval (-1,1).

cfS_Rectangular is an ALIAS of the more general function cf_RectangularSymmetric, used to evaluate the characteristic function of a linear combination of independent RECTANGULAR distributed random variables.

The characteristic function of X ~ RectangularSymmetric is defined by

cf(t) = sinc(t) = sin(t)/t.

Usage

cfS_Rectangular(t, coef, niid)

Arguments

t	vector or array of real values, where the CF is evaluated.
coef	vector of coefficients of the linear combination of Rectangular 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 the zero-mean symmetric RECTANGULAR distribution.

Note

Ver.: 16-Sep-2018 19:09:05 (consistent with Matlab CharFunTool v1.3.0, 02-Jun-2017 12:08:24).

References

WITKOVSKY V. (2016). Numerical inversion of a characteristic function: An alternative tool to form the probability distribution of output quantity in linear measurement models. Acta IMEKO, 5(3), 32-44.

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Uniform_distribution_(continuous).

Other Continuous Probability Distribution: cfS_Arcsine(), cfS_Beta(), cfS_Gaussian(), cfS_Laplace(), 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_Gaussian(), cfS_Laplace(), cfS_Student(), cfS_Trapezoidal(), cf_ArcsineSymmetric(), cf_BetaSymmetric(), cf_RectangularSymmetric(), cf_TSPSymmetric(), cf_TrapezoidalSymmetric()

Examples

## EXAMPLE1
# CF of the Rectangular distribution on (-1,1)
t <- seq(-50, 50, length.out = 501)
plotReIm(function(t)
        cfS_Rectangular(t), t, title = "CF of the Rectangular distribution on (-1,1)")

## EXAMPLE2
# PDF/CDF of the Rectangular distribution on (-1,1)
cf <- function(t)
        cfS_Rectangular(t)
x <- seq(-2, 2, length.out = 101)
xRange <- 2
options <- list()
options$N <- 2 ^ 5
options$dx <- 2 / pi / xRange
result <- cf2DistGP(cf = cf, x = x, options = options)

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