cfS_TSP: Characteristic function of the TWO-SIDED-POWER (TSP)...

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

Characteristic function of the TWO-SIDED-POWER (TSP) distribution with shape parameter theta > 0.

Description

cfS_TSP(t, theta, mu, sigma, coef, niid) is an ALIAS of the more general function cf_TSPSymmetric, used to evaluate the characteristic function of a linear combination of independent (location-scale) TSP distributed random variables.

The characteristic function of the random variable X ~ TSP(theta) is cf(t) = 1/2 * (hypergeom1F1(1,1+theta,1i*t) + hypergeom1F1(1,1+theta,-1i*t)).

#' SPECIAL CASES:
1) \theta = 1/2; Arcsine distribution on (-1,1): cf(t) = besselj(0,t),
2) \theta = 1; Rectangular distribution on (-1,1): cf(t) = sin(t)/t.

Usage

cfS_TSP(t, theta, mu, sigma, 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.
mu	vector of location parameters, mu in Real. If empty, default value is mu = 0.
sigma	vector of scale parameters, sigma_i > 0. If empty, default value is sigma = 1.
coef	vector of the coefficients of the linear combination of the log-transformed 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 n, such that Z = Y + ... + Y is sum of niid iid random variables Y, where each Y = sum_{i=1}^N coef(i) * log(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 (location scale TSP distributed random variables.

Note

Ver.: 11-Aug-2021 16:37:22 (consistent with Matlab CharFunTool v1.5.1, 24-Jun-2017 18:25:56).

References

[1] 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. [2] VAN DORP, R.J., KOTZ, S. (2003). Generalizations of two-sided power distributions and their convolution. Communications in Statistics-Theory and Methods, 32(9), 1703-1723.

See Also

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

Examples

## EXAMPLE 1
# CF of the symmetric TSP distribution with theta =3/2 on (-1,1)
theta <- 3/2
t <- seq(from = -50,
         to = 50,
         length.out =501)
plotReIm(function(t)
        cfS_TSP(t, theta),
        t,
        title = "CF of the symmetric TSP distribution  on (-1,1)")



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

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