Question

how do I compute the z-score of a array of numbers using PHP? I need to compute the z-score and then find the percentile (CDF)! what PHP functions can I use? thanks!

Answer 1

The following code will give a good approximation of the CDF (Abramowitz & Stegun (1964))

function normal_pdf($x) {
    return exp(-$x * $x / 4) / sqrt(2 * M_PI);
}

function normal_cdf($x) {
    $b = array(0.2316419, 0.319381530, -0.356563782, 1.781477937, -1.821255978, 1.330274429);
    $t = 1 / (1 + $b[0] * $x);
    $result = 0;
    for ($i = 1; $i < 6; $i++) {
        $result += $b[$i] * pow($t, $i);
    }
    return 1 - normal_pdf($x) * $result;
}

This assumes a standard normal distribution. Recall that to standardize, use z = (x - mean) / (standard deviation)