CharFun (version 0.1.0)

cfS_Trapezoidal: Characteristic function of Trapezoidal distribution

Description

cfS_Trapezoidal(t, a, c) (a > 0, c > 0, \(c \le a\)) evaluates the characteristic function cf(t) of the Trapezoidal distribution on the interval (-a, a) with mode on the interval (-c, c) (Trapezoidal distribution with mean = 0 and variance = ??? cfS_Trapezoidal(t, a, c) = (sin(w*at)/(w*at))*(sin((1-w)*at)/((1-w)*at))

Usage

cfS_Trapezoidal(t, a = 1, c = 1/3)

Arguments

t

numerical values (number, vector...)

a

number, a > 0, default value a = 1

c

number, (\(0 \le c \le a\)), default value c = 1/3

Value

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

See Also

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

Other Continuous Probability distribution: cfS_Arcsine, cfS_Beta, cfS_Gaussian, cfS_Rectangular, cfS_StudentT, cfS_Triangular, 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_Triangular

Examples

## EXAMPLE1 (CF of the Trapezoidal distribution with a = 1, c = 0.5)
t <- seq(-15, 15, length.out = 501)
plotGraf(function(t)
  cfS_Trapezoidal(t, c = 1 / 2), t,
  title = "CF of the Trapezoidal distribution with a = 1, c = 0.5")

## EXAMPLE2 (PDF/CDF of the compound Trapezoidal distribution with a = 1, c = 0.5)
cf <- function(t)
  cfS_Trapezoidal(t, c = 1 / 2)
x <- seq(-1, 1, length.out = 100)
prob <- c(0.9, 0.95, 0.99)
xRange <- 2
option <- list()
option$N <- 1000
option$dx <- 2 / pi / xRange
result <- cf2DistGP(cf, x, option = option)