CharFun (version 0.1.0)

cfX_Beta: Characteristic function of Beta distribution

Description

cfX_Beta(t,alpha, beta) evaluates the characteristic function cf(t) of the Beta distribution with the parameter alpha (shape, alpha > 0) and beta (shape, beta > 0) defined on the interval (0,1), i.e. beta distribution with the Mean = alpha / (alpha + beta) and the Variance = (alpha*beta) / ((alpha+beta)^2*(alpha+beta+1)). Then, the standard deviation is given by STD = sqrt(Variance) i.e. cf(t) = cfX_Beta(t,alpha,beta) = 1F1(alpha ,alpha + beta , i*t) where 1F1(.;.;.) is the Confluent hypergeometric function.

Usage

cfX_Beta(t, alpha = 1, beta = 1)

Arguments

t

numerical values (number, vector...)

alpha

shape, aplha > 0, default value aplha = 1

beta

shape, beta > 0, default value beta = 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_Beta, cfS_Gaussian, cfS_Rectangular, cfS_StudentT, cfS_Trapezoidal, cfS_Triangular, 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)