CharFun (version 0.1.0)

cfS_Triangular: Characteristic function of Triangular distribution

Description

cfS_Triangular(t, a) evaluates the characteristic function cf(t) of the Triangular distribution on the interval (-a, a) with mode 0 (Triangular distribution with mean = 0 and variance = 1/18(2a^2 + a) cfS_Triangula(t, a) = (2 - 2cos(at)) / (a^2 * t^2)

Usage

cfS_Triangular(t, a = 1)

Arguments

t

numerical values (number, vector...)

a

number, a > 0, default value a = 1

Value

characteristic function cf(t) of the Triangular distribution on the interval (-a, a) with mode 0

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Triangular_distribution

Other Continuous Probability distribution: cfS_Arcsine, cfS_Beta, cfS_Gaussian, cfS_Rectangular, cfS_StudentT, cfS_Trapezoidal, cfX_Beta, cfX_ChiSquared, cfX_Exponential, cfX_Gamma, cfX_InverseGamma, cfX_LogNormal, cfX_Normal, cfX_PearsonV, cfX_Rectangular, cfX_Triangular

Other Symetric Probability distribution: cfS_Arcsine, cfS_Gaussian, cfS_Rectangular, cfS_StudentT, cfS_Trapezoidal

Examples

## EXAMPLE1 (CF of the symmetric Triangular distribution on (-2 , 2))
t <- seq(-10, 10, length.out = 501)
plotGraf(function(t)
  cfS_Triangular(t, 2), t, title = "CF of the symmetric Triangular distribution on (-2 , 2)")

## EXAMPLE2 (PDF/CDF of the symmetric Triangular distribution on (-3 , 3))
cf <- function(t)
  cfS_Triangular(t, 3)
x <- seq(-3, 3, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
xRange <- 6
option <- list()
option$N <- 2 ^ 10
option$dx <- 2 / pi / xRange
result <- cf2DistGP(cf, x, option = option)