# نصب بسته‌های مورد نیاز
install.packages("ggplot2")
install.packages("fitdistrplus")

# بارگذاری بسته‌ها
library(ggplot2)
library(fitdistrplus)

# داده‌ها
data <- c(10.01, 3.76, 9.91, 7.40, 6.09, 6.60, 2.65, 2.52, 7.93, 4.97, 5.70, 1.08, 4.43, 2.90, 
          3.97, 4.64, 4.99, 5.49, 4.03, 6.11, 5.37, 3.54, 2.37, 3.19, 4.09, 4.48, 6.85, 
          7.09, 7.16, 4.67, 5.15)

# برازش توزیع Power Lomax
fit_pl <- fitdist(data, "lnorm")  # فرض می‌کنیم داده‌ها با توزیع لوگ-نرمال برازش داده شده‌اند

# نمودار تابع چگالی احتمال (PDF)
pdf_plot <- ggplot(data.frame(x = data), aes(x = x)) +
  geom_histogram(aes(y = ..density..), bins = 10, fill = "lightblue", color = "black", alpha = 0.6) +
  stat_function(fun = dlnorm, args = list(meanlog = fit_pl$estimate["meanlog"], sdlog = fit_pl$estimate["sdlog"]), color = "blue", size = 1) +
  labs(title = "Fitted PDF of the PL Distribution", x = "GDP Growth", y = "Density") +
  theme_minimal()

# نمودار تابع توزیع تجمعی (CDF)
cdf_plot <- ggplot(data.frame(x = data), aes(x = x)) +
  stat_ecdf(geom = "step", color = "darkgreen", size = 1) +
  stat_function(fun = plnorm, args = list(meanlog = fit_pl$estimate["meanlog"], sdlog = fit_pl$estimate["sdlog"]), color = "blue", size = 1) +
  labs(title = "Fitted CDF of the PL Distribution", x = "GDP Growth", y = "P(X <= x)") +
  theme_minimal()

# نمایش نمودارها
pdf_plot
cdf_plot
<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/frontend/web/index.php(18): yii\base\Application-&gt;run()
#11 {main}</pre>