cfS_Wigner: Characteristic function of a linear combination (resp....

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

Characteristic function of a linear combination (resp. convolution) of the zero-mean symmetric WIGNER distribution defined on the interval (-1,1).

Description

cfS_Wigner(t,coef,niid) is an ALIAS of the more general function cf_WignerSemicircle, used to evaluate the characteristic function of a linear combination of independent symmetric WIGNER SEMICIRCLE distributed random variables.

The characteristic function of the symmetric WIGNER distribution on (-1,1) is cf(t) = 2*besselj(1,t)/t.

Usage

cfS_Wigner(t, coef, niid)

Arguments

t	vector or array of real values, where the CF is evaluated.
coef	vector of the coefficients of the linear combination of the Beta 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 niid, such that Z = Y + ... + Y is sum of niid iid random variables Y, where each Y = sum_{i=1}^N coef(i) * X_i is independently and identically distributed random variable. If empty, default value is niid = 1.

Value

Characteristic function of a linear combination of independent symmetric WIGNER SEMICIRCLE distributed random variables.

Note

Ver.: 11-Aug-2021 15:51:34 (consistent with Matlab CharFunTool v1.5.1, 18-Sep-2018 00:45:54).

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/Wigner_semicircle_distribution.

Other Continuous Probability Distribution: cfS_Arcsine(), cfS_Beta(), cfS_Gaussian(), cfS_Laplace(), cfS_Rectangular(), cfS_Student(), cfS_TSP(), cfS_Trapezoidal(), cfS_Triangular(), 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()

Examples

## EXAMPLE 1
# CF of the symmetric Wigner distribution on (-1,1)
t <- seq(from = -50,
         to = 50,
         length.out =501)
plotReIm(function(t)
        cfS_Wigner(t),
        t,
        title = "CF of the Wigner distribution on (-1,1)")



##EXAMPLE2
# PDF/CDF of Wigner distribution on (-1,1)
cf <- function(t)
        cfS_Wigner(t)
x <- seq(-1,1,length.out = 501)
prob <- c(0.9, 0.95, 0.99)
options <- list()
options$xMin <- -1
options$xMax <- 1
result <- cf2DistGP(cf, x, prob, options)

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