CharFun (version 0.1.0)

cfS_Beta: Characteristic function of Beta distribution

Description

cfX_Beta(t,alpha, beta) evaluates the characteristic function cf(t) of the symmetric zero-mean Beta distribution with shape parameter theta >0, defined on the interval (-1,1), i.e. symmetric beta distribution with zero mean and variance VAR = 1/(1+2*theta). The standard deviation is given by STD = sqrt(1/(1+2*theta))), i.e. cf(t) = cfS_Beta(t,theta) = gamma(1/2+theta) * (t/2)^(1/2-theta) * besselj(theta-1/2,t). Special cases (for specific values of the shape parameter theta): 1) theta = 1/2; Arcsine distribution on (-1,1): cf(t) = besselj(0,t). 2) theta = 1; Rectangular distribution on (-1,1): cf(t) = sin(t)/t;

Usage

cfS_Beta(t, theta = 1)

Arguments

t

numerical values (number, vector...)

theta

default value theta = 1

Value

characteristic function cf(t) of the Beta distribution

See Also

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

Other Continuous Probability distribution: cfS_Arcsine, 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

Examples

## EXAMPLE1 (CF of the Beta distribution with alpha = 1/2, beta = 3/2)
alpha <- 1 / 2
beta <- 3 / 2
t <- seq(-50, 50, length.out = 501)
plotGraf(function(t)
  cfX_Beta(t, alpha, beta), t, title = "CF of the Beta distribution with alpha = 1/2, beta = 3/2")

## EXAMPLE2 (PDF/CDF of the Beta distribution with alpha = 1/2, beta = 3/2)
alpha <- 1 / 2
beta <- 3 / 2
cf <- function(t)
  cfX_Beta(t, alpha, beta)
x <- seq(0, 1, length.out = 101)
xRange <- 1
option <- list()
option$dx <- 2 * pi / xRange
result <- cf2DistGP(cf, x, option = option)