install.packages("nleqslv")
library(nleqslv)
# تابع توزیع تجمعی لوماکس توانی
cdfp1 <- function(x, alpha, beta, lambda) {
  1 - lambda^alpha * (lambda + x^beta)^(-alpha)
}
# تابع چگالی لوماکس توانی
pdfp1 <- function(x, alpha, beta, lambda) {
  alpha * beta * lambda^alpha * x^(beta - 1) * (lambda + x^beta)^(-alpha - 1)
}
x=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)

# مرتب سازی داده‌ها
x_sorted = sort(x)
n=length(x)
m=n
  # تعریف معادلات
  equationsML <- function(par) {
    alpha <- par[1]
    beta <- par[2]
    lambda <- par[3]
    
    # تعریف معادلات بر اساس مشتقات جزئی
    eqq1 <- sum(sapply(1:m, function(i) {
      1/alpha + log(lambda) - 2*log(lambda + x_sorted[i]^beta)
    }))
    
    eqq2 <- sum(sapply(1:m, function(i) {
      1/beta + log(x_sorted[i]) - (alpha + 1) * (x_sorted[i]^beta * log(x_sorted[i])) / (lambda + x_sorted[i]^beta)
    }))
    
    eqq3 <- sum(sapply(1:m, function(i) {
      alpha / lambda - (alpha + 1) / (lambda + x_sorted[i]^beta)
    }))
    
    # بازگشت مقادیر معادلات
    return(c(eqq1, eqq2, eqq3))
  }
  
  # مقدارهای اولیه برای پارامترها
  initial_guess <- c(1, 1, 1)
  
  # حل معادلات
  solution <- nleqslv(initial_guess, equationsML)
  
  # نمایش نتایج
  alphaML <- solution$x[1]
  betaML <- solution$x[2]
  lambdaML <- solution$x[3]


print(c(alphaML,
        betaML ,
        lambdaML))


cdfp1hat=function(x) cdfp1(x,5.4337,
                           2.904 ,
                           757.115)

# آزمون کولموگروف-اسمیرنوف
ks_test <- ks.test(x, cdfp1hat)
ks_test
# پارامترهای برآورد شده
alphaML <- 5.4337
betaML <- 2.904
lambdaML <- 757.115
# تابع لاگ-لایکلیهود
logLikPL <- function(x, alpha, beta, lambda) {
  pdf_values <- pdfp1(x, alpha, beta, lambda)
  log_likelihood <- sum(log(pdf_values))
  return(log_likelihood)
}
# محاسبه لاگ-لایکلیهود
logLikValue <- logLikPL(x, alphaML, betaML, lambdaML)

# تعداد پارامترهای مدل
k <- 3

# محاسبه AIC
AIC <- 2 * k - 2 * logLikValue
AIC

# محاسبه BIC
BIC <- log(n) * k - 2 * logLikValue
BIC

# محاسبه AICc
AICc <- AIC + (2 * k * (k + 1)) / (n - k - 1)
AICc

# محاسبه HQIC
HQIC <- -2 * logLikValue + 2 * k * log(log(n))
HQIC

<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>