cfS_Arcsine: Characteristic function of the symmetric zero-mean Arcsine...

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

Characteristic function of the symmetric zero-mean Arcsine distribution

Description

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

cfS_Arcsine is an ALIAS of the more general function cf_ArcsineSymmetric, used to evaluate the characteristic function of a linear combination of independent ARCSINE distributed random variables.

The characteristic function of the symmetric ARCSINE distribution is cf(t) = besselj(0,t).

Usage

cfS_Arcsine(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 Arcsine 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 Arcsine distribution.

Note

Ver.: 16-Sep-2018 19:06:57 (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/Arcsine_distribution.

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

Examples

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

## EXAMPLE2
# PDF/CDF of the symmetric Arcsine distribution on (-1,1)
cf <- function(t)
        cfS_Arcsine(t)
x <- seq(-1, 1, length.out = 501)
xRange <- 2
options <- list()
options$N <- 2 ^ 12
options$dt <- 2 * pi / xRange
result <- cf2DistGP(cf = cf, x = x, options = options)

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