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93 lines
3.4 KiB
PHP
93 lines
3.4 KiB
PHP
<?php
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function inverse_ncdf($p) {
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/***************************************************************************
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* inverse_ncdf.php
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* -------------------
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* begin : Friday, January 16, 2004
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* copyright : (C) 2004 Michael Nickerson
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* email : nickersonm@yahoo.com
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*
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***************************************************************************/
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//Inverse ncdf approximation by Peter John Acklam, implementation adapted to
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//PHP by Michael Nickerson, using Dr. Thomas Ziegler's C implementation as
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//a guide. http://home.online.no/~pjacklam/notes/invnorm/index.html
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//I have not checked the accuracy of this implementation. Be aware that PHP
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//will truncate the coeficcients to 14 digits.
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//You have permission to use and distribute this function freely for
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//whatever purpose you want, but please show common courtesy and give credit
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//where credit is due.
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//Input paramater is $p - probability - where 0 < p < 1.
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//Coefficients in rational approximations
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$a = array(1 => -3.969683028665376e+01, 2 => 2.209460984245205e+02,
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3 => -2.759285104469687e+02, 4 => 1.383577518672690e+02,
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5 => -3.066479806614716e+01, 6 => 2.506628277459239e+00);
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$b = array(1 => -5.447609879822406e+01, 2 => 1.615858368580409e+02,
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3 => -1.556989798598866e+02, 4 => 6.680131188771972e+01,
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5 => -1.328068155288572e+01);
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$c = array(1 => -7.784894002430293e-03, 2 => -3.223964580411365e-01,
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3 => -2.400758277161838e+00, 4 => -2.549732539343734e+00,
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5 => 4.374664141464968e+00, 6 => 2.938163982698783e+00);
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$d = array(1 => 7.784695709041462e-03, 2 => 3.224671290700398e-01,
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3 => 2.445134137142996e+00, 4 => 3.754408661907416e+00);
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//Define break-points.
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$p_low = 0.02425; //Use lower region approx. below this
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$p_high = 1 - $p_low; //Use upper region approx. above this
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//Define/list variables (doesn't really need a definition)
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//$p (probability), $sigma (std. deviation), and $mu (mean) are user inputs
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$q = NULL; $x = NULL; $y = NULL; $r = NULL;
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//Rational approximation for lower region.
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if (0 < $p && $p < $p_low) {
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$q = sqrt(-2 * log($p));
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$x = ((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q + $c[5]) *
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$q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) * $q + $d[4]) *
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$q + 1);
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}
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//Rational approximation for central region.
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elseif ($p_low <= $p && $p <= $p_high) {
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$q = $p - 0.5;
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$r = $q * $q;
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$x = ((((($a[1] * $r + $a[2]) * $r + $a[3]) * $r + $a[4]) * $r + $a[5]) *
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$r + $a[6]) * $q / ((((($b[1] * $r + $b[2]) * $r + $b[3]) * $r +
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$b[4]) * $r + $b[5]) * $r + 1);
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}
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//Rational approximation for upper region.
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elseif ($p_high < $p && $p < 1) {
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$q = sqrt(-2 * log(1 - $p));
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$x = -((((($c[1] * $q + $c[2]) * $q + $c[3]) * $q + $c[4]) * $q +
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$c[5]) * $q + $c[6]) / (((($d[1] * $q + $d[2]) * $q + $d[3]) *
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$q + $d[4]) * $q + 1);
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}
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//If 0 < p < 1, return a null value
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else {
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$x = NULL;
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}
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return $x;
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//END inverse ncdf implementation.
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}
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// Confidence level for binomial scoring. Just compute this once.
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define(Z_VAL, inverse_ncdf(1-(1-.95)/2));
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// Implementation of the algorithm described at http://www.evanmiller.org/how-not-to-sort-by-average-rating.html
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function binomial_score($Ups, $Total) {
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if (($Total <= 0) || ($Ups < 0)) {
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return 0;
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}
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$phat = $Ups/$Total;
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return ($phat + Z_VAL*Z_VAL/(2*$Total) - Z_VAL*sqrt(($phat*(1-$phat)+Z_VAL*Z_VAL/(4*$Total))/$Total))/(1+Z_VAL*Z_VAL/$Total);
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}
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?>
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