cfS_Laplace: Characteristic function of a symmetric Laplace distribution...

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

Characteristic function of a symmetric Laplace distribution with scale parameter beta>0.

Description

cfS_Laplace(t, beta, coef, niid) evaluates the characteristic function of a linear combination of independent (symmetric) Laplace distributed random variables.

That is, cfS_Laplace evaluates the characteristic function cf(t) of Y=sum_{i=1}^N coef_i * X_i, where X_i ~ Laplace (0,beta_i) are independent zero-mean RVs with the scale parameters beta_i > 0, for i = 1,...,N

Usage

cfS_Laplace(t, beta, coef, niid)

Arguments

t	vector or array of real values, where the CF is evaluated.
beta	vector of the scale parameters beta > 0. If empty, default value is beta = 1.
coef	vector of the coefficients of the linear combination of the LAPLACE 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 cf(t) of of a linear combination of independent (symmetric) LAPLACE sistributed random variables.

Note

Ver.: 10-Aug-2021 17:21:39 (consistent with Matlab CharFunTool v1.5.1, 16-Aug-2018 16:00:43).

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Normal_distribution.

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

Examples

## EXAMPLE 1
# CF of the linear combination of symmetric Laplace RV
beta <- 1
t <- seq(from = -10,
         to = 10,
         length.out =201)
plotReIm(function(t)
        cfS_Laplace(t, beta),
        t,
        title = "Characteristic function of the symmetric Laplace RV")



##EXAMPLE2
# PDF/CDF of the symmetric Laplace RVs
beta <- 1
x <- seq(-5, 5, length.out = 101)
prop <- c(0.80, 0.85, 0.90, 0.925, 0.95, 0.975, 0.99, 0.995, 0.999)
cf <- function(t)
        cfS_Laplace(t, beta)
result <- cf2DistGP(cf, x, prob)

##EXAMPLE3
# PDF/CDF of the linear combination of symmetric Laplace RVs
beta <- c(0.1, 0.2, 0.3, 0.4)
coef <- c(1, 2, 3, 4)
prop <- c(0.80, 0.85, 0.90, 0.925, 0.95, 0.975, 0.99, 0.995, 0.999)
cf <- function(t)
        cfS_Laplace(t, beta, coef)
options <- list()
options$N <- 2^12
result <- cf2DistGP(cf, c(), prob, options)

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