Confusion Equation(X Equation) with normal distribution (PHP- Laravel)

calcXEq.php

<?        
       // From 2006 to 2019
       $years = config('years');
 
      // Get All normal distribution records of bankrupted companies for selected Country
      $allBankruptedCompaniesCount = NormalDistribution::join('companies AS c', 'company_id', '=', 'c.id')
            ->where('c.country', '=', 'UK')
            ->where('c.bankrupted', '=', 'yes')
            ->get()->unique('company_id')
            ->count();
 
 
        \Cache::flush();
 
        // initiatal values
        $plus = 0.00;
        $row1All = [];
        $row3All = [];
        $rowResult = [];
 
        // Mimic percentages; from 1% to 100%
        for ($i = 1; $i <= 100; $i++) {
            
            $plus += 0.01;
            // reset values for each percentage
            $countOfBankruptedCompaniesForPercentage = 0;
            $countOfHealthyCompaniesForPercentage = 0;
            
            // for every year
            foreach ($years as $year) {
                
                // Get every normal distribution record of given country
                // in given year and sort them by ascending order
                $normDist = NormalDistribution::join('companies AS c', 'company_id', '=', 'c.id')
                    ->where('c.country', '=', 'UK')
                    ->where('year', '=', $year)->get()
                    ->sortBy('value', SORT_NUMERIC);
                
                // get normal distribution as many records based on current percentage
                // i.e; 1 percent = Take 1 percent of all records in given condition
                $normDistForThatPercentage = $normDist->take(round($normDist->count() * $plus, 0, PHP_ROUND_HALF_DOWN));
 
                // separate bankrupted and healthy companies from the records above ($normDistForThatPercentage)
                $bankruptedCompaniesOfTheYear = $normDistForThatPercentage->where('bankrupted', 'yes')->unique('company_id');
                $healthyCompaniesOfTheYear = $normDistForThatPercentage->where('bankrupted', 'no')->unique('company_id');
 
                // Add numbers and store to the variables respectively.
                // This will help us determine the bankrupted and healthy company numbers for the percentage.
                $countOfBankruptedCompaniesForPercentage += $bankruptedCompaniesOfTheYear->count();
                $countOfHealthyCompaniesForPercentage += $healthyCompaniesOfTheYear->count();
            }
 
            // store same values under the given key for later use.
            // ie; in some equation, a value from previous percentage is needed.
            // storing them in a separate storage and using them will ease the process
            \Cache::put($i.'bankrupted-percentage', $countOfBankruptedCompaniesForPercentage);
            \Cache::put($i.'non-bankrupted-percentage', $countOfHealthyCompaniesForPercentage);
 
            if ($i === 1) {
                // for 1% row one is as follows
                $row1 = $countOfHealthyCompaniesForPercentage;
            } else {
                // for 2% until 100% $row1 is stored as count of healthy companies for that percentage minus the value previous percentage.
                // this will help us achieve isolate the difference instead of the accumulated numbers.
                $row1 = $countOfHealthyCompaniesForPercentage - \Cache::get($i - 1 . 'non-bankrupted-percentage');
            }
            
            // self explanatory
            $row2 = $allBankruptedCompaniesCount - $countOfBankruptedCompaniesForPercentage;
 
            // see $row1. Same principle but with bankrupted companies.
            if ($i === 1) {
                $row3 = $countOfBankruptedCompaniesForPercentage;
            } else {
                $row3 = $countOfBankruptedCompaniesForPercentage - \Cache::get($i - 1 . 'bankrupted-percentage');
            }
            
            // self explanatory
            if ($i === 1) {
                $row4 = 0;
            } else {
                $row4 = $countOfHealthyCompaniesForPercentage; // note that this includes all records for the given percentage.
            }
 
            // store the values in arrays respectively for each percentage
            $row1All[] = $row1;
            $row2All[] = $row2;
            $row3All[] = $row3;
            $row4All[] = $row4;
            
            // store the result of the equation in the array for each percentage
            $rowResult[] = $row1 * $row2 + 0.5 * $row1 * $row3;
        }
 
 
        // get the sum of the all values and store them respectively
        $rowResult = array_sum($rowResult);
        $row3All = array_sum($row3All);
        $row1All = array_sum($row1All);
 
        // calculate auc
        $auc = $rowResult / ($row3All * $row1All);
 
        // calculate q1
        $q1 = $auc / (2 - $auc);
 
        // calculate q2
        $q2 = 2 * ($auc * $auc) / (1 + $auc);
 
        // calculate se
        $se = sqrt(($auc * (1 - $auc) + ($row3All - 1) * ($q1 - ($auc * $auc)) + ($row1All - 1) * ($q2 - ($auc * $auc))) / ($row3All * $row1All));
        
        // calculate z
        $z = ($auc - 0.5) / $se;
        
        // calculate ar
        $ar = 2 * ($auc - 0.5);
 
        // store the results
        $results = [
            'auc' => $auc, 'se' => $se, 'z' => $z, 'AR' => $ar,
        ];
        
       
        return $results;