CharFun (version 0.1.0)

cfX_Exponential: Characteristic function of Exponential distribution

Description

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

cfX_Exponential(t, lambda) = lambda / (lambda - it)

Usage

cfX_Exponential(t, lambda = 1)

Arguments

t

numerical values (number, vector...)

lambda

rate, lambda > 0, default value lambda = 1

Value

characteristic function cf(t) of the Exponential distribution

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_Rectangular, cfS_StudentT, cfS_Trapezoidal, cfS_Triangular, cfX_Beta, cfX_ChiSquared, cfX_Gamma, cfX_InverseGamma, cfX_LogNormal, cfX_Normal, cfX_PearsonV, cfX_Rectangular, cfX_Triangular

Examples

## EXAMPLE1 (CF of the Exponential distribution with lambda = 5)
lambda <- 5
t <- seq(-10, 10, length.out = 501)
plotGraf(function(t)
  cfX_Exponential(t, lambda), t, title = "CF of the Exponential distribution with lambda = 5")

## EXAMPLE2 (PDF/CDF of the Exponential distribution with lambda = 5)
lambda <- 5
cf <- function(t)
  cfX_Exponential(t, lambda)
x <- seq(0, 1.5, length.out = 501)
result <- cf2DistGP(cf, x, SixSigmaRule = 8, xMin = 0)

## EXAMPLE3 (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(0, 5, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, isCompound = TRUE)