#EB landa ML gama ML s(t) h(t) در مدل سوم
library(actuar)
my_func <- function(){
  
  # تعریف پارامترها و مقداردهی اولیه
  shape1 <- 2
  shape2 <- 1
  n <- 50
  m <- 20
  
  # تولید داده‌ها از توزیع Burr و مرتب‌سازی آن‌ها
  y <- sort(rburr(n, shape1, shape2))
  
  # انتخاب داده‌های اولیه
  x <- y[1:m]
  
  # تعریف مقدار T1 و T2
  T1 <- 0.5
  T2 <- 1
  
  # تنظیم Rs بر اساس مدل سوم
  Rs <- numeric(n)
  Rs[1] <- Rs[m] <- (n - m) / 2
  
  # تعریف سایر مقادیر Rs به صفر
  Rs[-c(1, m)] <- 0
  
  # تعریف سایر متغیرها
  ds <- 0
  Rsd1 <- 0
  Rsd2 <- 0
  
  # تنظیم ds بر اساس شرط‌های موردنظر
  if (x[m] > T1 & x[m] < T2) {
    ds <- m
    Rsd1 <- 0
    Rsd2 <- 0
  } else if (x[m] > T2) {
    ds <- which.max(x[x < T2])
    x <- x[1:ds]
    Rsd2 <- n - ds
  } else if (x[m] < T1) {
    ds <- which.max(y[y < T1])
    x <- y[1:ds]
    Rsd1 <- n - ds
  }
  
  # تنظیم پارامترهای برآورد lambda و gamma
  gama=array(100)
  lamda=array(100)
  gama[1] <- 1
  
  # حلقه محاسبه gamma و lambda
  for (j in 1:99) {
    lamda[j] <- ds / (sum(sapply(1:ds, function(i) (Rs[i] + 1) * log(1 + x[i]^gama[j]))) + Rsd1 * log(1 + T1^gama[j]) + Rsd2 * log(1 + T2^gama[j]))
    
    denom <- sum(sapply(1:ds, function(i) (lamda[j] * (Rs[i] + 1) + 1) * x[i]^gama[j] * log(x[i]) / (1 + x[i]^gama[j]))) + lamda[j] * (Rsd1 * T1^gama[j] * log(T1^gama[j]) / (1 + T1^gama[j]) + Rsd2 * T2^gama[j] * log(T2^gama[j]) / (1 + T2^gama[j])) - sum(log(x[1:ds]))
    
    if (is.nan(denom)) {
      denom <- rnorm(1)
    }
    
    gama[j + 1] <- ds / denom
    
    if (abs(gama[j + 1] - gama[j]) < 0.01) {
      break
    }
  }
  
  # برآورد نهایی gamahat و lamdahat
  gamahat <- gama[length(gama)]
  lamdahat <- ds / (sum(sapply(1:ds, function(i) (Rs[i] + 1) * log(1 + x[i]^gamahat))) + Rsd1 * log(1 + T1^gamahat) + Rsd2 * log(1 + T2^gamahat))
  shat=(1+0.5^gamahat)^(-lamdahat)
  hhat=lamdahat*gamahat*0.5^(gamahat-1)*(1+0.5^gamahat)^(-1)
  
  # برگرداندن مقادیر برآورد شده
  return(c(gamahat, lamdahat,shat,hhat))
}

# انجام شبیه‌سازی و جمع‌آوری نتایج
b <- replicate(10000, my_func())

# جداسازی مقادیر gamma و lambda
gam <- b[1,]
lam <- b[2,]
shaat=b[3,]
hhaat=b[4,]

# فیلتر کردن مقادیر gamma و lambda در محدوده 0 تا 5
gam_filtered <- gam[gam >= 0 & gam <= 5]
lam_filtered <- lam[lam >= 0 & lam <= 5]

# شمارش تعداد مقادیر فیلتر شده
count_gam_filtered <- length(gam_filtered)
count_lam_filtered <- length(lam_filtered)

# چاپ تعداد مقادیر فیلتر شده
print(paste("تعداد عناصر gam_filtered:", count_gam_filtered))
print(paste("تعداد عناصر lam_filtered:", count_lam_filtered))

a<- gam_filtered[-c(1:2000)]
a
c<- lam_filtered[-c(1:2000)]
c

actual_gamahat <- 1
actual_lamdahat <- 2

# محاسبه EB برای هر یک از پارامترها
EB_shaat <- mean(shaat) - actual_lamdahat
EB_hhaat <- mean(hhaat) - actual_gamahat
EB_a <- mean(a) - actual_gamahat
EB_c <- mean(c) - actual_lamdahat

# چاپ نتایج
print(paste("Expected Bias for shaat (EB_shaat):", EB_shaat))
print(paste("Expected Bias for hhaat (EB_hhaat):", EB_hhaat))
print(paste("Expected Bias for a (EB_a):", EB_a))
print(paste("Expected Bias for c (EB_c):", EB_c))

<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>