function calculate_variance($data_set = array())
{
$mean = calculate_mean($data_set);
$squared_sum = 0.0;
foreach ($data_set as $data_point) {
$deviation_from_mean = $data_point - $mean;
$squared_sum += pow($deviation_from_mean, 2);
}
return $squared_sum / count($data_set);
}
/**
* The mean of the beta deviates B(a,b) should be about equal to a/(a+b).
*
* E[B(a,b)] = a / (a + b)
*/
public function testBetaDistributionMean()
{
$a = rand($this->a_minimum, $this->a_maximum);
$b = rand($this->b_minimum, $this->b_maximum);
$data_points = array();
for ($i = 0; $i < $this->number_of_samples; ++$i) {
$data_points[] = generate_random_beta_variate($a, $b);
}
$expected_mean = $a / ($a + $b);
$beta_mean = calculate_mean($data_points);
$this->assertEquals(round($expected_mean, $this->precision), round($beta_mean, $this->precision), "The mean of the beta deviates does not equal a/(a+b)");
}
