Description Usage Arguments Value See Also Examples
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)
1 | cfX_Exponential(t, lambda = 1)
|
t |
numerical values (number, vector...) |
lambda |
rate, lambda > 0, default value lambda = 1 |
characteristic function cf(t) of the Exponential distribution
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ## 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)
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