# CFLib.org – Common Function Library Project

## CND(x)

##### Last updated March 10, 2003

Version: 1 | Requires: CF5 | Library: MathLib

Description:
Computes cumulative normal distribution function.

Return Values:
Returns a numeric value.

Example:

``````<cfoutput>
CND(3) = #CND(3)#
</cfoutput>
``````

Parameters:

Name Description Required
x value for which you want to compute the cumulative normal distribution Yes

Full UDF Source:

``````/**
* Cumulative Normal Distribution
*
* @param x      value for which you want to compute the cumulative normal distribution (Required)
* @return Returns a numeric value.
* @author Alex (axs@arbornet.org)
* @version 1, March 10, 2003
*/
function CND (x) {
// The cumulative normal distribution function
var Pi = 3.141592653589793238;
var a1 = 0.31938153;
var a2 = -0.356563782;
var a3 = 1.781477937;
var a4 = -1.821255978;
var a5 = 1.330274429;
var L = abs(x);
var k = 1 / ( 1 + 0.2316419 * L);
var p = 1 - 1 /  ((2 * Pi)^0.5) * exp( -(L^2) / 2 ) * (a1 * k + a2 * (k^2) + a3 * (k^3) + a4 * (k^4) + a5 * (k^5) );

if (x gte 0)
return p;
else
return 1-p;

}
``````

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