cfX_Exponential: Characteristic function of the EXPONENTIAL distribution

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

Characteristic function of the EXPONENTIAL distribution

Description

cfX_Exponential(t, lambda) evaluates characteristic function of the EXPONENTIAL distribution with the rate parameter lambda > 0.

cfX_Exponential is an ALIAS NAME of the more general function cf_Exponential, used to evaluate the characteristic function of a linear combination

of independent EXPONENTIAL distributed random variables. The characteristic function of the EXPONENTIAL distribution is

cf(t) = \lambda / (\lambda - 1i*t).

Usage

cfX_Exponential(t, lambda, coef, niid)

Arguments

t	vector or array of real values, where the CF is evaluated.
lambda	vector of the 'rate' parameters lambda > 0. If empty, default value is lambda = 1.
coef	vector of coefficients of the linear combination of Exponentially 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 EXPONENTIAL distribution.

Note

Ver.: 16-Sep-2018 19:21:37 (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/Exponential_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_ChiSquare(), 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 Exponential distribution with lambda = 5
lambda <- 5
t <- seq(from = -50,
         to = 50,
         length.out = 501)
plotReIm(function(t)
        cfX_Exponential(t, lambda), t, title = "CF of the Exponential distribution with lambda = 5")

## EXAMPLE 2
# PDF/CDF of the Exponential distribution with lambda = 5
lambda <- 5
cf <- function(t)
        cfX_Exponential(t, lambda)
x  <- seq(from = 0,
          to = 1.5,
          length.out = 101)
options <- list()
options$xMin <- 0
options$SixSigmaRule <- 8
result <- cf2DistGP(cf = cf, x = x, options = options)

## EXAMPLE 3
# PDF/CDF of the compound Binomial-Exponential distribution
n <- 25
p <- 0.3
lambda <- 5
cfX <- function(t)
        cfX_Exponential(t, lambda)
cf <- function(t)
        cfN_Binomial(t, n, p, cfX)
x <- seq(from = 0,
         to = 5,
         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.