R/Examples/example_cf_InverseGamma.R

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

## EXAMPLE 1
# CF of a linear combination of K=100 independent IGamma 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' ~ chi ^ 2 ~ 'RVs with DF=1')
)
lines(1:50, coef, col = "blue")
alpha <- 5 / 2
beta <- 2
t <- seq(from = -100,
         to = 100,
         length.out = 201)
plotReIm(function(t)
        cf_InverseGamma(t, alpha, beta, coef), t,
        title = "Characteristic function of the linear combination of IGamma 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_InverseGamma(t, alpha, beta, coef)
options <- list()
options$N <- 2 ^ 10
options$xMin = 0
x <- seq(from = 0,
         to = 4,
         length.out = 201)
prob <- c(0.9, 0.95, 0.99)
result <- cf2DistGP(cf, x, prob, options)
result