private static function _inverse_ncdf($p)
{
// Inverse ncdf approximation by Peter J. Acklam, implementation adapted to
// PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
// a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
// I have not checked the accuracy of this implementation. Be aware that PHP
// will truncate the coeficcients to 14 digits.
// You have permission to use and distribute this function freely for
// whatever purpose you want, but please show common courtesy and give credit
// where credit is due.
// Input paramater is $p - probability - where 0 < p < 1.
// Coefficients in rational approximations
static $a = array(1 => -39.69683028665376, 2 => 220.9460984245205, 3 => -275.9285104469687, 4 => 138.357751867269, 5 => -30.66479806614716, 6 => 2.506628277459239);
static $b = array(1 => -54.47609879822406, 2 => 161.5858368580409, 3 => -155.6989798598866, 4 => 66.80131188771972, 5 => -13.28068155288572);
static $c = array(1 => -0.007784894002430293, 2 => -0.3223964580411365, 3 => -2.400758277161838, 4 => -2.549732539343734, 5 => 4.374664141464968, 6 => 2.938163982698783);
static $d = array(1 => 0.007784695709041462, 2 => 0.3224671290700398, 3 => 2.445134137142996, 4 => 3.754408661907416);
// Define lower and upper region break-points.
$p_low = 0.02425;
//Use lower region approx. below this
$p_high = 1 - $p_low;
//Use upper region approx. above this
if (0 < $p && $p < $p_low) {
// Rational approximation for lower region.
$q = sqrt(-2 * log($p));
return ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
} elseif ($p_low <= $p && $p <= $p_high) {
// Rational approximation for central region.
$q = $p - 0.5;
$r = $q * $q;
return ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) * $r + $a[6]) * $q / ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r + $b[4]) * $r + $b[5]) * $r + 1);
} elseif ($p_high < $p && $p < 1) {
// Rational approximation for upper region.
$q = sqrt(-2 * log(1 - $p));
return -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) * $q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) * $q + 1);
}
// If 0 < p < 1, return a null value
return PHPExcel_Calculation_Functions::NULL();
}
public function testNULL()
{
$result = PHPExcel_Calculation_Functions::NULL();
$this->assertEquals('#NULL!', $result);
}
