install.packages("mvtnorm")
install.packages("moments")

library(mvtnorm)
library(moments)

set.seed(123)

n <- 1000
m <- 5000

params_df <- data.frame(
  mu1 = c(-1, -1, -0.5, -0.5, -0.5, 0, 0, 0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 2, -1, 0, 0, 0, 0, 2, 2, 1),
  mu2 = c(-1, -1, -0.5, -0.5, -0.5, 0, 0, 0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 1, 2, 0, 2, 2, -1, 2, 2, 2, 2),
  sigma1 = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 0.5, 0.5, 2),
  sigma2 = c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 0.5, 2, 1, 1, 1, 0.5),
  rho = c(0, 1, 0, 0.5, 1, 0, 0.5, 1, 0, 0.5, 1, 0, 0.5, 1, 0, 0, 0.5, 1, 0.5, 0.5, 1, 0.5, 0.5, 1),
  a = c(0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 2, 2, 2, 0.5, 0.5, 2, 0.5, 0.5, 1, 0.5, 2, 2, 0.5),
  b = c(0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, 2, 2, 2, 0.5, 0.5, 0.5, 2, 0.5, 0.5, 2, 2, 2, 2)
)

results <- data.frame()

for (i in 1:nrow(params_df)) {
  mu1 <- params_df$mu1[i]
  mu2 <- params_df$mu2[i]
  sigma1 <- params_df$sigma1[i]
  sigma2 <- params_df$sigma2[i]
  rho <- params_df$rho[i]
  a <- params_df$a[i]
  b <- params_df$b[i]
  sigma_mat <- matrix(c(sigma1^2, rho * sigma1 * sigma2,
                        rho * sigma1 * sigma2, sigma2^2), nrow = 2)
  stats <- matrix(NA, nrow = m, ncol = 10)
  colnames(stats) <- c("mean_X", "mean_Y", "mean_XY", "var_X", "var_Y", "cov_XY", "skew_X", "skew_Y", "kurt_X", "kurt_Y")
  for (j in 1:m) {
    UV <- rmvnorm(n, mean = c(mu1, mu2), sigma = sigma_mat)
    U <- UV[, 1]
    V <- UV[, 2]
    X <- log(1 + exp(U)) / a
    Y <- log(1 + exp(V)) / b
    stats[j, 1] <- mean(X)
    stats[j, 2] <- mean(Y)
    stats[j, 3] <- mean(X * Y)
    stats[j, 4] <- var(X)
    stats[j, 5] <- var(Y)
    stats[j, 6] <- cov(X, Y)
    stats[j, 7] <- skewness(X)
    stats[j, 8] <- skewness(Y)
    stats[j, 9] <- kurtosis(X)
    stats[j, 10] <- kurtosis(Y)
  }
  avg_stats <- colMeans(stats, na.rm = TRUE)
  results <- rbind(results, c(params_df[i, ], avg_stats))
}

colnames(results) <- c(colnames(params_df), "Mean_X", "Mean_Y", "Mean_XY", "Var_X", "Var_Y", "Cov_XY", "Skew_X", "Skew_Y", "Kurt_X", "Kurt_Y")

print(results)

round(print(results),4)
<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>