note 88558 modified in function.stats-stat-percentile by danbrown
| From: | danbrown@php.net | Date: | Wed, 24 Feb 2010 16:09:12 +0000 |
| Subject: | note 88558 modified in function.stats-stat-percentile by danbrown | ||
| References: | 1 | Groups: | php.notes |
| Request: | Send a blank email to php-notes+get-166320@lists.php.net to get a copy of this message | ||
If you are looking to infer the percentile from a z-score, you can use this function.
It's far from precise but does the job on most circumstances.
The error function ( erf() )is based on the approximation on wikipedia:
http://en.wikipedia.org/wiki/Error_function
<?php
function erf($x)
{
$pi = 3.1415927;
$a = (8*($pi - 3))/(3*$pi*(4 - $pi));
$x2 = $x * $x;
$ax2 = $a * $x2;
$num = (4/$pi) + $ax2;
$denom = 1 + $ax2;
$inner = (-$x2)*$num/$denom;
$erf2 = 1 - exp($inner);
return sqrt($erf2);
}
function cdf($n)
{
if($n < 0)
{
return (1 - erf($n / sqrt(2)))/2;
}
else
{
return (1 + erf($n / sqrt(2)))/2;
}
}
// EXAMPLE
$sample = 90;
$avg = 75;
$stddev = 12;
$zscore = ($sample - $avg) / $stddev;
print 'Percentile: ' . cdf($zscore) * 100 . "\n";
?>
Where $n is the z-score
The function cdf() returns the approximed cumulative standard normal distribution ([0..1])
[EDIT BY danbrown AT php DOT net: Contains a bugfix provided by (Ed) on 24-FEB-2010 which fixes the
definition of $a in erf() with the note that it is "out by a factor of -1" in the original
code.]
--was--
If you are looking to infer the percentile from a z-score, you can use this function.
It's far from precise but does the job on most circumstances.
The error function ( erf() )is based on the approximation on wikipedia:
http://en.wikipedia.org/wiki/Error_function
<?php
function erf($x)
{
$pi = 3.1415927;
$a = (8*($pi - 3))/(3*$pi*($pi - 4));
$x2 = $x * $x;
$ax2 = $a * $x2;
$num = (4/$pi) + $ax2;
$denom = 1 + $ax2;
$inner = (-$x2)*$num/$denom;
$erf2 = 1 - exp($inner);
return sqrt($erf2);
}
function cdf($n)
{
if($n < 0)
{
return (1 - erf($n / sqrt(2)))/2;
}
else
{
return (1 + erf($n / sqrt(2)))/2;
}
}
// EXAMPLE
$sample = 90;
$avg = 75;
$stddev = 12;
$zscore = ($sample - $avg) / $stddev;
print 'Percentile: ' . cdf($zscore) * 100 . "\n";
?>
Where $n is the z-score
The function cdf() returns the approximed cumulative standard normal distribution ([0..1])
http://php.net/manual/en/function.stats-stat-percentile.php