cfS_Beta: Characteristic function of the zero-mean symmetric BETA...

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

Characteristic function of the zero-mean symmetric BETA distribution

Description

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

cfS_Beta is an ALIAS of the more general function cf_BetaSymmetric, used to evaluate the characteristic function of a linear combination of independent BETA distributed random variables.

The characteristic function of X ~ BetaSymmetric(\theta) is defined by

cf(t) = cf_BetaSymmetric(t,\theta) = gamma(1/2+\theta) * (t/2)^(1/2-\theta) * besselj(\theta-1/2,t).

Usage

cfS_Beta(t, theta = 1, coef, niid)

Arguments

t	vector or array of real values, where the CF is evaluated.
theta	the 'shape' parameter theta > 0. If empty, default value is theta = 1.
coef	vector of coefficients of the linear combination of 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.

Value

Characteristic function cf(t) of the Beta distribution.

Note

Ver.: 16-Sep-2018 19:07:26 (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/Beta_distribution.

Other Continuous Probability Distribution: cfS_Arcsine(), 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_Arcsine(), 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 Beta distribution with theta = 3/2 on (-1,1)
theta <- 3 / 2
t <- seq(-50, 50, length.out = 501)
plotReIm(function(t)
        cfS_Beta(t, theta), t, title = "CF of the symmetric Beta distribution on (-1,1)")

## EXAMPLE2
# PDF/CDF of the the symmetric Beta distribution on (-1,1)
theta <- 3 / 2
cf <- function(t)
        cfS_Beta(t, theta)
x <- seq(-1, 1, length.out = 101)
xRange <- 2
options <- list()
options$dx <- 2 * pi / xRange
options$N <- 2 ^ 8
result <- cf2DistGP(cf = cf, x = x, options = options)

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