cfS_Rectangular: Characteristic function of Rectangular distribution

In CharFun: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

Description

cfS_Rectangular(t) evaluates the characteristic function cf(t) of the symmetric zero-mean Rectangular distribution on the interval (-a, a) (Rectangular distribution with mean = 0 and variance = 1/3*a^2) cfS_Rectangular(t, a) = sin(at)/at

Usage

cfS_Rectangular(t, a = 1)

Arguments

t	numerical values (number, vector...)
a	number, a > 0, default value a = 1

Value

characteristic function cf(t) of the Rectangular distribution on the interval (-a, a)

See Also

For more details see WIKIPEDIA: https://en.wikipedia.org/wiki/Uniform_distribution_(continuous)

Other Continuous Probability distribution: cfS_Arcsine, cfS_Beta, cfS_Gaussian, cfS_StudentT, cfS_Trapezoidal, 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_StudentT, cfS_Trapezoidal, cfS_Triangular

Examples

## EXAMPLE1 (CF of the Rectangular distribution on (-1,1))
t <- seq(-50, 50, length.out = 501)
plotGraf(function(t)
  cfS_Rectangular(t), t, title = "CF of the Rectangular distribution on (-1,1)")

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

## EXAMPLE3 (PDF/CDF of the Rectangular distribution on (-1,1))
cf <- function(t)
  cfS_Rectangular(t)
x <- seq(-1, 1, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf,
                    x,
                    prob,
                    xMin = -1,
                    xMax = 1,
                    N = 2)

CharFun documentation built on May 2, 2019, 9:18 a.m.