R/Examples/example_cf_Gamma.R

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

## EXAMPLE 1
# CF of a linear combination of independent Gamma RVs
coef <- 1 / (((1:50) - 0.5) * pi) ^ 2
plot(
        1:50,
        coef,
        xlab = "",
        ylab = "",
        type = "p",
        pch = 20,
        col = "blue",
        cex = 1,
        main = expression('Coefficients of the linear combination of GAMMA RVs')
)
lines(1:50, coef, col = "blue")
alpha <- 5 / 2
beta <- 1 / 2
t <- seq(from = -10,
         to = 10,
         length.out = 201)
plotReIm(function(t)
        cf_Gamma(t, alpha, beta, coef),
        t,
        title = "Characteristic function of the linear combination of GAMMA RVs")

## EXAMPLE 2
# PDF/CDF from the CF by cf2DistGP
alpha <- 5 / 2
beta <- 1 / 2
coef <- 1 / (((1:50) - 0.5) * pi) ^ 2
cf <- function(t)
        cf_Gamma(t, alpha, beta, coef)
options <- list()
options$N <- 2 ^ 10
options$xMin <- 0
result <- cf2DistGP(cf = cf, options = options)