_Normdist ( z ; mu ; sigma )

FileMaker implementation of NORMDIST Excel function

Average rating: 4.7 (31 votes) Log in to vote

Mislav Kos - Show more from this author
Soliant Consulting
https://www.soliantconsulting.com/

Sample input:

( 100; 100; 15 )
( 90 ; 100; 15 )
( 70 ; 100; 15 )
( 130; 100; 15 )

Sample output:

0.500000001
0.252492467
0.022750062
0.977249938

Compare to Excel
0.500000000
0.252492538
0.022750132
0.977249868

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

/**
 * @SIGNATURE:
 * _Normdist ( z ; mu ; sigma )
 * 
 * @PARAMETERS:
 * z - The parameter for which the cumulative probability is calculated for.
 * mu - The mean (i.e. average).
 * sigma - The standard deviation. Note: Sigma must be greater than 0.
 * 
 * @HISTORY:
 * Created: 2011-Aug-30 by Mislav Kos, Soliant Consulting
 * 
 * @PURPOSE: 
 * To provide a near equivalent of the NORMDIST Excel function, for when its "cumulative" parameter is set to true.
 * 
 * @RESULT:
 *  The cumulative probability that the observed value of a normal random variable with mean mu and standard deviation sigma will be less than or equal to parameter z.
 * 
 * @ERRORS:
 * N/A
 * 
 * @DEPENDENCIES:
 * This custom function requires the _Normsdist ( z ) custom function.
 * 
 * @NOTES:
 * 
 * This custom function is a FileMaker implementation of the NORMDIST function in Excel.
 * Caution: This custom function is ONLY AN APPROXIMATION of the Excel function; 
 * i.e. it will calculate an approximate answer rather than the exact answer.
 * (Note: The same is true of the Excel function.)
 * The results are accurate to several decimal places, which is typically sufficient for most uses.
 * 
 * Also see the custom function _Normsdist ( z ).
 * 
 * The difference between NORMDIST and NORMSDIST:
 *   - NORMSDIST applies to standard normal distribution.
 *   - NORMDIST applies to any normal distribution.
 *   - A standard normal distribution has a mean of 0 and a standard deviation of 1.
 * 
 * The calculation was adapted from http://www.wilmott.com/messageview.cfm?catid=8&threadid=78622.
 * 
 * Here are some notes on the NORMDIST Excel function from http://support.microsoft.com/kb/827371: 
 *   - The normal distribution is a continuous probability distribution whose shape is determined by its mean, mu, and standard deviation, sigma. 
 *   - The normal distribution with mean mu and standard deviation sigma is centered at mu and has half of its probability to the left of mu and half to the right.
 *   - The /standard/ normal distribution is the special case where mu = 0 and sigma = 1.
 *   - The probability is distributed according to the familiar bell-shaped curve with the total area under the curve equal to 1.
 *   - The probability that a value that is less than or equal to z will occur (also called cumulative probability up to z) is the area under this curve to the left of z.
 *   - In NORMDIST, when the last argument is set to TRUE, NORMDIST returns the cumulative probability that the observed value of a Normal random variable with mean mu and standard deviation sigma will be less than or equal to z.
 * 
 */


_Normsdist ( 

	( z - mu ) / sigma 

)

PURPOSE:
To provide a near equivalent of the NORMDIST Excel function, for when its "cumulative" parameter is set to true.

RESULT:
The cumulative probability that the observed value of a normal random variable with mean mu and standard deviation sigma will be less than or equal to parameter z.

DEPENDENCIES:
This custom function requires the _Normsdist ( z ) custom function.

NOTES:
This custom function is a FileMaker implementation of the NORMDIST function in Excel.
Caution: This custom function is ONLY AN APPROXIMATION of the Excel function;
i.e. it will calculate an approximate answer rather than the exact answer.
(Note: The same is true of the Excel function.)
The results are accurate to several decimal places, which is typically sufficient for most uses.

Also see the custom function _Normsdist ( z ).

The difference between NORMDIST and NORMSDIST:
- NORMSDIST applies to standard normal distribution.
- NORMDIST applies to any normal distribution.
- A standard normal distribution has a mean of 0 and a standard deviation of 1.

The calculation was adapted from http://www.wilmott.com/messageview.cfm?catid=8&threadid=78622.

Here are some notes on the NORMDIST Excel function from http://support.microsoft.com/kb/827371:
- The normal distribution is a continuous probability distribution whose shape is determined by its mean, mu, and standard deviation, sigma.
- The normal distribution with mean mu and standard deviation sigma is centered at mu and has half of its probability to the left of mu and half to the right.
- The /standard/ normal distribution is the special case where mu = 0 and sigma = 1.
- The probability is distributed according to the familiar bell-shaped curve with the total area under the curve equal to 1.
- The probability that a value that is less than or equal to z will occur (also called cumulative probability up to z) is the area under this curve to the left of z.
- In NORMDIST, when the last argument is set to TRUE, NORMDIST returns the cumulative probability that the observed value of a Normal random variable with mean mu and standard deviation sigma will be less than or equal to z.

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Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

_Normdist ( z ; mu ; sigma )

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