install.packages("copula")
install.packages("psych")
install.packages("gridExtra")
install.packages("ggplot2")

library(copula)
library(psych)
library(gridExtra)
library(ggplot2)

generate_bfgmtlee <- function(n, alpha1, lambda1, alpha2, lambda2, delta) {
  cop <- fgmCopula(param = delta, dim = 2)
  u <- rCopula(n, copula = cop)
  x <- -log(1 - u[,1]^(1/alpha1)) / (2 * lambda1)
  y <- -log(1 - u[,2]^(1/alpha2)) / (2 * lambda2)
  return(data.frame(x = x, y = y))
}

set.seed(123)
data1 <- generate_bfgmtlee(n = 5500, alpha1 = 3, lambda1 = 0.7, alpha2 = 5, lambda2 = 0.9, delta = -0.9)
data2 <- generate_bfgmtlee(n = 5500, alpha1 = 0.3, lambda1 = 0.7, alpha2 = 0.5, lambda2 = 0.9, delta = 0.1)
data3 <- generate_bfgmtlee(n = 5500, alpha1 = 0.3, lambda1 = 0.7, alpha2 = 0.5, lambda2 = 0.9, delta = 0.6)
data4 <- generate_bfgmtlee(n = 7000, alpha1 = 3, lambda1 = 0.7, alpha2 = 5, lambda2 = 0.9, delta = 0.9)

panel_hist_paper <- function(x, n_breaks = 15, col_fill = "#FFC0CB", ...) {
  usr <- par("usr"); on.exit(par(usr = usr))
  h <- hist(x, plot = FALSE, breaks = n_breaks)
  d <- density(x, na.rm = TRUE)
  ymax <- 1.05 * max(h$density, d$y, na.rm = TRUE)
  par(usr = c(range(x, finite = TRUE), 0, ymax))
  rect(h$breaks[-length(h$breaks)], 0, h$breaks[-1], h$density,
       col = col_fill, border = "black")
  lines(d$x, d$y, lwd = 1, col = "black")
  rug(x, col = "black")
  box()
}
panel_cor_tr <- function(x, y, ...) {
  usr <- par("usr"); on.exit(par(usr=usr))
  par(usr=c(0,1,0,1))
  text(.5, .5, formatC(cor(x, y), digits=2, format="f"), cex=2)
}
panel_scatter <- function(x, y, ...) {
  points(x, y, pch=16, cex=.55, col="black")
  lines(lowess(x, y), col="red", lwd=2)
  points(mean(x, na.rm=TRUE), mean(y, na.rm=TRUE), pch=19, col="red", cex=1.6)
}


pairs(data1,
      lower.panel = panel_scatter,
      upper.panel = panel_cor_tr,
      diag.panel  = function(x, ...) panel_hist_paper(x, n_breaks = 15),
      labels = c("x","y"))
pairs(data2,
      lower.panel = panel_scatter,
      upper.panel = panel_cor_tr,
      diag.panel  = function(x, ...) panel_hist_paper(x, n_breaks = 15),
      labels = c("x","y"))
pairs(data3,
      lower.panel = panel_scatter,
      upper.panel = panel_cor_tr,
      diag.panel  = function(x, ...) panel_hist_paper(x, n_breaks = 15),
      labels = c("x","y"))
pairs(data4,
      lower.panel = panel_scatter,
      upper.panel = panel_cor_tr,
      diag.panel  = function(x, ...) panel_hist_paper(x, n_breaks = 15),
      labels = c("x","y"))<pre>An Error occurred while handling another error:
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Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/ErrorHandler.php(136): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/ErrorHandler.php(135): yii\web\ErrorHandler-&gt;renderException()
#3 [internal function]: yii\base\ErrorHandler-&gt;handleException()
#4 {main}
Previous exception:
yii\web\HeadersAlreadySentException: Headers already sent in  on line 0. in /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php:366
Stack trace:
#0 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Response.php(339): yii\web\Response-&gt;sendHeaders()
#1 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(656): yii\web\Response-&gt;send()
#2 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/models/Files.php(696): yii\base\Application-&gt;end()
#3 /var/www/html/prof-homepages/vendor/faravaghi/yii2-filemanager/controllers/FilesController.php(484): faravaghi\filemanager\models\Files-&gt;getFile()
#4 [internal function]: faravaghi\filemanager\controllers\FilesController-&gt;actionGetFile()
#5 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/InlineAction.php(57): call_user_func_array()
#6 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Controller.php(180): yii\base\InlineAction-&gt;runWithParams()
#7 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Module.php(528): yii\base\Controller-&gt;runAction()
#8 /var/www/html/prof-homepages/vendor/yiisoft/yii2/web/Application.php(103): yii\base\Module-&gt;runAction()
#9 /var/www/html/prof-homepages/vendor/yiisoft/yii2/base/Application.php(386): yii\web\Application-&gt;handleRequest()
#10 /var/www/html/prof-homepages/backend/web/index.php(16): yii\base\Application-&gt;run()
#11 {main}</pre>