cfS_Triangular: Characteristic function of the zero-mean symmetric TRIANGULAR...

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

Characteristic function of the zero-mean symmetric TRIANGULAR distribution

Description

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

cfS_Triangular is an ALIAS of the more general function cf_TriangularSymmetric, used to evaluate the characteristic function of a linear combination of independent TRIANGULAR distributed random variables.

The characteristic function of X ~ TriangularSymmetric is defined by

cf(t) = (2-2*cos(t))/t^2.

Usage

cfS_Triangular(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 Triangular 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 TRIANGULAR distribution.

Note

Ver.: 16-Sep-2018 19:11:08 (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/Triangular_distribution.

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

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.: cf_TriangularSymmetric()

Examples

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

## EXAMPLE 2
# PDF/CDF of the the symmetric Triangular distribution on (-1,1)
cf <- function(t)
        cfS_Triangular(t)
x <- seq(from = -1,
         to = 1,
         length.out = 101)
xRange <- 2
options <- list()
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.