R Under development (unstable) (2025-09-21 r88861 ucrt) -- "Unsuffered Consequences"
Copyright (C) 2025 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> # Clean environment and load libraries
> rm(list = ls())  # Clear environment to avoid conflicts
> 
> # Source files
> library(MixStable)

Attaching package: 'MixStable'

The following object is masked from 'package:graphics':

    clip

> library(ggplot2)
> 
> # 🎲 Generate data
> set.seed(123)
> X <- rnorm(300)
> u_vals <- seq(-10, 10, length.out = 200)
> 
> # 🔍 Compute ECF using recursive method
> ecf_result <- ecf_fn(X, u_vals, method = "recursive")
> yr <- ecf_result$magnitude
> 
> # 🔍 Compute ECF using kernel method
> ecf_result1 <- ecf_fn(X, u_vals, method = "kernel")
> yr1 <- ecf_result1$magnitude
> 
> # 📊 Plot kernel-smoothed ECF
> df_plot1 <- data.frame(u = u_vals, magnitude = yr1)
> 
> p1 <- ggplot(df_plot1, aes(x = u, y = magnitude)) +
+   geom_line(color = "blue") +
+   labs(
+     title = "Empirical Characteristic Function (Kernel Smoothed)",
+     x = "u (frequency)",
+     y = "|ECF(u)|"
+   ) +
+   theme_minimal()
> 
> # 📊 Plot recursive-smoothed ECF
> df_plot <- data.frame(u = u_vals, magnitude = yr)
> 
> p <- ggplot(df_plot, aes(x = u, y = magnitude)) +
+   geom_line(color = "red") +
+   labs(
+     title = "Empirical Characteristic Function (Recursive Smoothed)",
+     x = "u (frequency)",
+     y = "|ECF(u)|"
+   ) +
+   theme_minimal()
> 
> # Show plots
> print(p1)
> print(p)
> 
> # Save the plots
> ggsave("ecf_kernel_plot.png", p1, width = 10, height = 5, dpi = 300)
> ggsave("ecf_recursive_plot.png", p, width = 10, height = 5, dpi = 300)
> 
> proc.time()
   user  system elapsed 
  16.95    1.67   18.62