R/Examples/example_cf_Beta.R

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

## EXAMPLE 1
# CF of a Beta RV
alpha <- 1
beta  <- 3
t <- seq(from = -50,
         to = 50,
         length.out = 501)
plotReIm(function(t)
        cf_Beta(t, alpha, beta), t, title = "CF of a Beta RVs")

## EXAMPLE 2
# PDF/CDF of a Beta RV
alpha <- 1
beta  <- 3
cf <- function(t) {
        cf_Beta(t, alpha, beta)
}
options <- list()
options$N <- 2 ^ 12
options$xMin <- 0
options$xMax <- 1
x <- seq(from = 0,
         to = 1,
         length.out = 201)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, options)

## EXAMPLE 3
# CF of a linear combination of independent Beta RVs
alpha <- 1
beta  <- 3
coef  <- 1 / (((1:50) - 0.5) * pi) ^ 2
weights <- coef / sum(coef)
t <- seq(from = -100,
         to = 100,
         length.out = 501)
plotReIm(function(t)
        cf_Beta(t, alpha, beta, weights),
        t,
        title = "CF of a weighted linear combination of independent Beta RVs")

## EXAMPLE 4
# PDF/CDF of a weighted linear combination of independent Beta RVs
alpha <- 1
beta  <- 3
coef  <- 1 / (((1:50) - 0.5) * pi) ^ 2
weights <- coef / sum(coef)
cf <- function(t) {
        cf_Beta(t, alpha, beta, weights)
}
options <- list()
options$xMin <- 0
options$xMax <- 1
x <- seq(from = 0,
         to = 1,
         length.out = 201)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, options)