QuantileNormal ( mean ; standardDeviation ; p )

Inverse normal cumulative distribution function

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Jeremy Bante

https://github.com/jbante/

Sample input:

List (
QuantileNormal ( 1 ; 2 ; .3 ) ;
QuantileNormal ( 3 ; 2 ; .1 ) ;
QuantileNormal ( 4 ; 6 ; .7 ) ;
QuantileNormal ( 8 ; 9 ; .4 ) ;
QuantileNormal ( "" ; "" ; .999 )
)

Sample output:

-.0488010254160816
.4368968689108328
7.1464030762482447
5.7198760717778018
2.9860384446470287

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

/**
 * =====================================
 * QuantileNormal ( mean ; standardDeviation ; p )
 * https://github.com/jbante/FileMaker-Techniques/blob/master/CustomFunctions/Math/QuantileNormal.fmfn
 *
 * RETURNS:
 *		The value from the specified normal distribution such that other values
 *		sampled from the same distribution fall below that value with p
 *		probability. This is sometimes known as the probit function in other
 *		programming environments.
 *
 * PARAMETERS:
 *		mean: The mean of a normal distribution. Defaults to 0 (standard normal
 *		distribution) if left empty.
 *		standardDeviation: The standardDeviation of a normal distribution.
 *		Defaults to 1 (standard normal distribution) if left empty.
 *		p: The cumulative probability at the desired quantile
 *
 * DEPENDENCIES:
 *		ErrorFunctionInverse ( x )
 *
 * HISTORY:
 *		CREATED on 2013-03-12 by Jeremy Bante <http://scr.im/jbante>.
 *
 * REFERENCES:
 *		http://en.wikipedia.org/wiki/Normal_distribution
 *		http://en.wikipedia.org/wiki/Error_function#Related_functions
 * =====================================
 */

If ( p ≤ 0 or p ≥ 1 ;	// out of bounds
	"?" ;
/* Else */
	Sqrt ( 2 )
	* ErrorFunctionInverse ( 2 * p - 1 )
	* If ( IsEmpty ( standardDeviation ) ; 1 ; /* Else */ standardDeviation )
	+ If ( IsEmpty ( mean ) ; 0 ; /* Else */ mean )
)

Returns the value from the specified normal distribution such that other values sampled from the same distribution fall below that value with p probability. This is sometimes known as the probit function in other programming environments.

This function is dependent on the ErrorFunctionInverse custom function.

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QuantileNormal ( mean ; standardDeviation ; p )

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