Description Usage Arguments Value See Also Examples
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;
1 |
t |
numerical values (number, vector...) |
theta |
default value theta = 1 |
characteristic function cf(t) of the Beta distribution
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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | ## 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)
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