php statistics z-score normal distributions - php

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)

Answer 2

/* Mean */
function mean($input_array)
{
$total = 0;
foreach ($input_array as $value)
{
$total += $value;
}
return ($total / count($input_array));
}
/* Standard Deviation */
function std($arr)
{
if (!count($arr))
return 0;
$mean = mean($arr);
$sos = 0; // Sum of squares
for ($i = 0; $i < count($arr); $i++)
{
$sos += ($arr[$i] - $mean) * ($arr[$i] - $mean);
}
return sqrt($sos / (count($arr) - 1));
}
/* Z Scores */
function z($var, $arr)
{
return ($var -mean($arr)) / std($arr);
}

Answer 3

There are a few functions in the PHP statistics extension that could help you — You probably want stats_standard_deviation for a start.

Answer 4

$control=array(15,7);
$treatment=array(46,8);
$confidence=number_format(cumnormdist(zscore($control, $treatment))*100,0);
function cr($t)
{
return $t[1]/$t[0];
}
function zscore($c, $t)
{
$z = cr($t)-cr($c);
$s = (cr($t)*(1-cr($t)))/$t[0] + (cr($c)*(1-cr($c)))/$c[0];
return $z/sqrt($s);
}
function cumnormdist($x)
{
$b1 = 0.319381530;
$b2 = -0.356563782;
$b3 = 1.781477937;
$b4 = -1.821255978;
$b5 = 1.330274429;
$p = 0.2316419;
$c = 0.39894228;
if($x >= 0.0) {
$t = 1.0 / ( 1.0 + $p * $x );
return (1.0 - $c * exp( -$x * $x / 2.0 ) * $t *
( $t *( $t * ( $t * ( $t * $b5 + $b4 ) + $b3 ) + $b2 ) + $b1 ));
}
else {
$t = 1.0 / ( 1.0 - $p * $x );
return ( $c * exp( -$x * $x / 2.0 ) * $t *
( $t *( $t * ( $t * ( $t * $b5 + $b4 ) + $b3 ) + $b2 ) + $b1 ));
}
}