CharFun (version 0.1.0)

cfS_Arcsine: Characteristic function of symmetric zero-mean Arcsine distribution

Description

cfS_Arcsine(t) evaluates the characteristic function cf(t) of the symmetric zero-mean Arcsine distribution on the interval (-1,1) (U-shaped distribution with mean = 0 and variance = 1/2 $$cfS_Arcsine(t) = besselj(0,t)$$

Usage

cfS_Arcsine(t)

Arguments

t

numerical values (number, vector...)

Value

characteristic function cf(t) of the Arcsine distribution

See Also

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

Other Continuous Probability distribution: 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, cfX_Triangular

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

Examples

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

## EXAMPLE2 (PDF/CDF of the symmetric Arcsine distribution on (-1,1))
cf <- function(t)
  cfS_Arcsine(t)
x <- seq(-1, 1, length.out = 501)
prob <- c(0.9, 0.95, 0.99)
xRange <- 2
N <- 2 ^ 12
option <- list()
option$dt <- 2 * pi / xRange
result <- cf2DistGP(cf, x, prob, option, N = N)