CharFun (version 0.1.0)

cfX_Triangular: Characteristic function of Triangular distribution

Description

cfX_Triangular(t, a, b, c) (\(a \le c \le b\)) evaluates the characteristic function cf(t) of the Triangular distribution on the interval (a, b) with mode c (Triangular distribution with mean = a + b + c)/3 and variance = 1/18(a^2 + b^2 + c^2 + - ab - ac - bc)) cfX_Triangula(t, a, b, c) = -2((b-c)exp(iat) - (b-a)exp(ict) + (c-a)exp(ibt))/((b-a)(c-a)(b-c)t^2)

Usage

cfX_Triangular(t, a = -1, b = 1, c = 0)

Arguments

t

numerical values (number, vector...)

a

number, default value a = -1

b

number, default value b = 1

c

number, (\(a \le c \le b\)), default value c = 0

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/Triangular_distribution

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

Examples

## EXAMPLE1 (CF of the Triangular distribution on (-1 , 2) mode = 0)
t <- seq(-10, 10, length.out = 501)
plotGraf(function(t)
  cfX_Triangular(t, a = -1, b = 2, c = 0), t,
  title = "CF of the Triangular distribution on (-1 , 2)")

## EXAMPLE2 (PDF/CDF of the Triangular distribution on (-1 , 2) mode = 0)
cf <- function(t)
  cfX_Triangular(t, a = -1, b = 2, c = 0)
x <- seq(-1, 2, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
xRange <- 3
option <- list()
option$N <- 2 ^ 10
option$dx <- 2 / pi / xRange
result <- cf2DistGP(cf, x, option = option)