cfX_ChiSquare: Characteristic function of the CHI-SQUARE distribution

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

Characteristic function of the CHI-SQUARE distribution

Description

cfX_ChiSquare(t, df, ncp, coef, niid) evaluates the characteristic function cf(t) of the CHI-SQUARE distribution with df > 0 degrees of freedom and the non-cetrality parameter ncp > 0.

cfX_ChiSquare is an ALIAS NAME of the more general function cf_ChiSquare, used to evaluate the characteristic function of a linear combination of independent CHI-SQUARE distributed random variables.

The characteristic function of the CHI-SQUARE distribution is defined by

cf(t) = (1 - 2*i*t )^(df/2) * exp((i*t*ncp)/(1-2*i*t)).

Usage

cfX_ChiSquare(t, df, ncp, coef, niid)

Arguments

t	vector or array of real values, where the CF is evaluated.
df	the degrees of freedom parameter df > 0. If empty, default value is df = 1.
ncp	the non-centrality parameter ncp > 0. If empty, default value is ncp = 0.
coef	vector of coefficients of the linear combination of Chi-square 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 CHI-SUQARE distribution.

Note

Ver.: 16-Sep-2018 19:20:45 (consistent with Matlab CharFunTool v1.3.0, 24-Jun-2017 10:07:43).

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Chi-squared_distribution.

Other Continuous Probability Distribution: cfS_Arcsine(), cfS_Beta(), cfS_Gaussian(), cfS_Laplace(), cfS_Rectangular(), cfS_Student(), cfS_TSP(), cfS_Trapezoidal(), cfS_Triangular(), cfS_Wigner(), 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 ChiSquared distribution with df = 1
df <- 1
t <- seq(from = -50,
         to = 50,
         length.out = 501)
plotReIm(function(t)
        cfX_ChiSquare(t, df), t, title = "CF of the Chi-square distribution with df = 1")

## EXAMPLE 2
# PDF/CDF of the ChiSquare distribution with df = 3
df <- 3
x <- seq(from = 0,
         to = 15,
         length.out = 101)
prob <- c(0.9, 0.95, 0.99)
cf <- function(t)
        cfX_ChiSquare(t, df)
options <- list()
options$xMin <- 0
options$N <- 2 ^ 14
result <- cf2DistGP(cf, x, prob, options)

## EXAMPLE 3
# PDF/CDF of the compound Binomial-ChiSquared distribution
n <- 25
p <- 0.3
df <- 3
cfX <- function(t)
        cfX_ChiSquare(t, df)
cf <- function(t)
        cfN_Binomial(t, n, p, cfX)
x <- seq(from = 0,
         to = 80,
         length.out = 101)
prob <- c(0.9, 0.95, 0.99)
options <- list()
options$isCompound <- TRUE
result <- cf2DistGP(cf, x, prob, options)

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