CFLib.org – Common Function Library Project

inverseNorms(v)

Last updated March 7, 2009

Version: 0 | Requires: CF5 | Library: MathLib

Description:
Generally calculating Inverse norms is via a lookup table. This is very slow and for a lage data set requires alot of static data and a complex look up structure. This is converted to Coldfusion but the mathematics was produced by Peter J. Acklam from: http://home.online.no/~pjacklam/notes/invnorm/

Return Values:
returns inverse of a number

Example:

``````<!--- number must be > 0 and < 1 --->
<cfset aNumber = 0.04 />
<cfoutput>Inverse Norm of #aNumber# = #inverseNorms(aNumber)#</cfoutput>``````

Parameters:

Name Description Required
v Numeric between 0 and 1 Yes

Full UDF Source:

``````/**
* Calculating the inverse normal cumulative distribution function
*
* @param v 	 Numeric between 0 and 1 (Required)
* @return returns inverse of a number
* @author Paul Kukiel (kukielp@gmail.com)
* @version 0, March 7, 2009
*/
function inverseNorms(v){

var a1 = -39.69683028665376;
var a2 = 220.9460984245205;
var a3 = -275.9285104469687;
var a4 = 138.3577518672690;
var a5 = -30.66479806614716;
var a6 = 2.506628277459239;

var b1 = -54.47609879822406;
var b2 = 161.5858368580409;
var b3 = -155.6989798598866;
var b4 = 66.80131188771972;
var b5 = -13.28068155288572;

var c1 = -0.007784894002430293;
var c2 = -0.3223964580411365;
var c3 = -2.400758277161838;
var c4 = -2.549732539343734;
var c5 = 4.374664141464968;
var c6 = 2.938163982698783;

var d1 = 0.007784695709041462;
var d2 = 0.3224671290700398;
var d3 = 2.445134137142996;
var d4 = 3.754408661907416;

var p_low = 0.02425;
var p_high = 1 - p_low;
var q = 0;
var r = 0;
var result = 0;

//Rational approximation for lower region
if((0 lt arguments.v) and  (arguments.v lt p_low)){
q = sqr(-2*log(arguments.v));
result = (((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q+c6) / ((((d1*q+d2)*q+d3)*q+d4)*q+1);
//Rational approximation for central region
}else{
if((p_low lte arguments.v) and (arguments.v lte p_high )){
q = arguments.v - 0.5;
r = q*q;
result = (((((a1*r+a2)*r+a3)*r+a4)*r+a5)*r+a6)*q / (((((b1*r+b2)*r+b3)*r+b4)*r+b5)*r+1);
//Rational approximation for upper region
}else{
if((p_high lt arguments.v) and (arguments.v lt 1)){
q = sqr(-2*log(1-arguments.v));
result = -(((((c1*q+c2)*q+c3)*q+c4)*q+c5)*q+c6) / ((((d1*q+d2)*q+d3)*q+d4)*q+1);
}
}
}

return result;
}``````
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