install.packages("copula")
install.packages("plot3D")
install.packages("reshape2")
install.packages("ggplot2")

library(copula)
library(plot3D)
library(reshape2)
library(ggplot2)

cdf_bfgmtlee <- function(x, y, alpha1, lambda1, alpha2, lambda2, delta) {
  G1 <- 1 - exp(-2 * lambda1 * x)
  G2 <- 1 - exp(-2 * lambda2 * y)
  u <- G1^alpha1
  v <- G2^alpha2
  cdf <- u * v + delta * u * v * (1 - u) * (1 - v)
  return(cdf)
}

pdf_bfgmtlee <- function(x, y, alpha1, lambda1, alpha2, lambda2, delta) {
  G1 <- 1 - exp(-2 * lambda1 * x)
  G2 <- 1 - exp(-2 * lambda2 * y)
  g1 <- 2 * lambda1 * exp(-2 * lambda1 * x)
  g2 <- 2 * lambda2 * exp(-2 * lambda2 * y)
  u <- G1^alpha1
  v <- G2^alpha2
  du_dx <- alpha1 * G1^(alpha1 - 1) * g1
  dv_dy <- alpha2 * G2^(alpha2 - 1) * g2
  copula_density <- 1 + delta * (1 - 2 * u) * (1 - 2 * v)
  pdf <- du_dx * dv_dy * copula_density
  return(pdf)
}

alpha1 <- 3; lambda1 <- 0.7
alpha2 <- 5; lambda2 <- 0.9
delta <- 0.9

x_seq <- seq(0, 5, length.out = 50)
y_seq <- seq(0, 5, length.out = 50)
grid <- expand.grid(x = x_seq, y = y_seq)
grid$cdf <- mapply(cdf_bfgmtlee, grid$x, grid$y,
                   MoreArgs = list(alpha1 = alpha1, lambda1 = lambda1,
                                   alpha2 = alpha2, lambda2 = lambda2, delta = delta))
grid$pdf <- mapply(pdf_bfgmtlee, grid$x, grid$y,
                   MoreArgs = list(alpha1 = alpha1, lambda1 = lambda1,
                                   alpha2 = alpha2, lambda2 = lambda2, delta = delta))
z_cdf <- matrix(grid$cdf, nrow = 50, byrow = TRUE)

persp(x_seq, y_seq, z_cdf, theta = -30, phi = 30,expand = 0.75,
        cex.axis = 0.65,cex.lab  = 0.95,
        xlab = "x", ylab = "y", zlab = "F(x,y)",ticktype = "detailed",
        main = "", col = "#00FFFF",border = "black")
contour(x_seq, y_seq, z_cdf,
        xlab = "x", ylab = "y", main = "",col = heat.colors(20), lwd = 3)
####################################
x_seq <- seq(0, 3, length.out = 50)
y_seq <- seq(0, 3, length.out = 50)
grid <- expand.grid(x = x_seq, y = y_seq)
grid$cdf <- mapply(cdf_bfgmtlee, grid$x, grid$y,
                   MoreArgs = list(alpha1 = alpha1, lambda1 = lambda1,
                                   alpha2 = alpha2, lambda2 = lambda2, delta = delta))
grid$pdf <- mapply(pdf_bfgmtlee, grid$x, grid$y,
                   MoreArgs = list(alpha1 = alpha1, lambda1 = lambda1,
                                   alpha2 = alpha2, lambda2 = lambda2, delta = delta))
z_pdf <- matrix(grid$pdf, nrow = 50, byrow = TRUE)

persp(x_seq, y_seq, z_pdf, theta = -33, phi = 30,expand = 0.65,
        cex.axis = 0.65,cex.lab  = 0.95,
        xlab = "x", ylab = "y", zlab = "f(x,y)",ticktype = "detailed",
        main = "", col = "#00FFFF",border = "black")
contour(x_seq, y_seq, z_pdf,
        xlab = "x", ylab = "y", main = "",col = heat.colors(20), lwd = 3)

<pre>An Error occurred while handling another error:
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/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>