/**
* Calculate the outliers for a dataset using
* 'Standard Deviation around the mean'.
*
* Steps:
* 1. Calculate the mean and the std
* 2. Calculate the top and bottom thresholds
* 3. It a value is over the top or under the bottom value,
* then it is an outlier.
*
* @param array $data
* @param number $mean_thres
*/
public static function outlierAroundMean(array $data, $mean_thres = 2)
{
$outliers = [];
// Step 1.
$mean = Basic::mean($data);
$std = Error::std($data);
// Step 2.
$top = $mean + $mean_thres * $std;
$bottom = $mean - $mean_thres * $std;
// Step 3.
foreach ($data as $item) {
if ($item > $top || $item < $bottom) {
array_push($outliers, $item);
}
}
return $outliers;
}
/**
* Calculates the 'Simple Moving Average' for a data set.
*
* Steps:
* 1. Make sure elements are numeric
* 2. 'Moving Average Value' can't be greater than the size of the elements.
* In such case set the value to the size of the elements.
* 3. Calculate the number of the Moving Average calculated elements.
* 4. Initiate the array to be returned with null values.
* 5. Calculate the Moving Average values:
* 1. Calculate new array with the needed elements, based on the given 'Moving Average Value'
* 2. Calculate the mean
* 3. Add it to the array
*
* @param number $ma_value Moving Average Value
* @param array $data Data Set
*/
public static function simpleMovingAverage($ma_value, $data = [])
{
// Step 1.
array_map("self::isNumeric", $data);
// Step 2.
$ma_value = self::fixMaValue(count($data), $ma_value);
// Step 3.
$ma_calc_items = count($data) - $ma_value + 1;
// Step 4.
$ma_arr = array_pad([], count($data), null);
// Step 5.
for ($i = 0; $i < $ma_calc_items; $i++) {
// Step 5.1.
$arr = array_slice($data, $i, $ma_value);
// Step 5.2.
$mean = Basic::mean($arr);
// Step 5.3
$ma_arr[$i + $ma_value - 1] = $mean;
}
return $ma_arr;
}
/**
* Calculates the variance for a data set for a pupulation or a sample set.
* Variance is defined as 'The average of the squared differences from the Mean.'.
*
* References:
* http://www.mathsisfun.com/data/standard-deviation.html
*
* Steps:
* 1. Make sure that elements are numeric
* 2. Calculate the mean
* 3. Calculate the variance : the 'Mean Squared Error' between the elements and the mean
*
* @param array $data
*/
public static function variance($data = [], $population = true)
{
$variance = 0;
// Step 1.
array_map("self::isNumeric", $data);
// Step 2.
$mean = Basic::mean($data);
// Step 3.
$n = count($data);
$sum = 0;
for ($i = 0; $i < $n; $i++) {
$sum += pow(self::absoluteError($data[$i], $mean), 2);
}
if ($population == true) {
$variance = round($sum / $n, 3);
} else {
$variance = round($sum / ($n - 1), 3);
}
return $variance;
}