R/Examples/example_cfE_Empirical.R

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

## EXAMPLE1
# Empirical CF - a weighted mixture of independent Dirac variables
set.seed(101)
n <- 1000
data <- c(rnorm(3 * n, 5, 0.2), rt(n, 3), rchisq(n, 1))
t <- seq(-50, 50, length.out = 2 ^ 10)
plotReIm(function(t)
        cfE_Empirical(t, data),
        t,
        title = "Empirical CF - CF of the mixture of Dirac random variables")

## EXAMPLE2
# Convolution of the ECF and the Gaussian kernel)
set.seed(101)
n <- 1000
data <- c(rnorm(3 * n, 5, 0.2), rt(n, 3), rchisq(n, 1))
bandwidth <- 0.25
cf_DATA   <- function(t)
        cfE_Empirical(t, data)
cf_KERNEL <- function(t)
        exp(-(bandwidth * t) ^ 2 / 2)
cf <- function(t)
        cf_DATA(t) * cf_KERNEL(t)
t <- seq(-50, 50, length.out = 2 ^ 10)
plotReIm(cf, t, title = "Smoothed Empirical CF")
result <- cf2DistGP(cf)

## EXAMPLE3
# (PDF/CDF of the compound Empirical-Empirical distribution)
set.seed(101)
lambda <- 25
nN <- 10
Ndata <- rpois(nN, lambda)

mu <- 0.1
sigma <- 2
nX <- 1500
Xdata <- rlnorm(nX, mu, sigma)
cfX <- function(t)
        cfE_Empirical(t, Xdata)
cf  <- function(t)
        cfE_Empirical(t, Ndata, cfX)
t <- seq(-0.2, 0.2, length.out = 2 ^ 10)
plotReIm(cf, t, title = "Compound Empirical CF")

x <- seq(0, 1000, length.out = 501)
prob <- c(0.9, 0.95)
options <- list()
options$N <- 2 ^ 10
options$SixSigmaRule <- 10
result <- cf2DistGP(cf, x, prob, options)