R/Examples/example_cfX_LogNormal.R

In CharFun: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

# EXAMPLE1 (CF of the Lognormal distribution with mu = 0,sigma = 1)
mu <- 0
sigma <- 1
t <- seq(-20, 20, length.out = 2 ^ 10 + 1)
plotGraf(function(t)
  cfX_LogNormal(t, mu, sigma), t, title = "Characteristic function of the Lognormal distribution")

# EXAMPLE2 (CDF/PDF of the Lognormal distribution with mu = 0,sigma = 1)
mu <- 0
sigma <- 1
x <- seq(0, 15, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
cf <- function(t)
  cfX_LogNormal(t, mu, sigma)
result <-
  cf2DistGP(cf,
            x,
            prob,
            N = 2 ^ 10,
            SixSigmaRule = 8,
            xMin = 0)

# EXAMPLE3 (PDF/CDF of the compound Poisson-Lognormal distribution)
mu <- 0
sigma <- 1
lambda <- 10
x <- seq(0, 70, length.out = 101)
prob <- c(0.9, 0.95, 0.99)
cfX <- function(t)
  cfX_LogNormal(t, mu, sigma)
cf <- function(t)
  cfN_Poisson(t, lambda, cfX)
result <- cf2DistGP(cf, x, prob, isCompound = TRUE, N = 2 ^ 10)