

Grasshopper
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Is there an equivalent of Excel's NORMDIST function in SQL Server 2005?




SSChampion
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Grasshopper
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Last Login: Tuesday, January 13, 2015 11:40 AM
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If it helps anyone, this is how my function looks like. Thanks again to all who helped me.
CREATE FUNCTION [dbo].[udf_NORMDIST](@value FLOAT, @mean FLOAT, @sigma FLOAT, @cummulative BIT) RETURNS NUMERIC(28,8) AS /**************************************************************************************** NAME: udf_NORMDIST WRITTEN BY: Tim Pickering http://www.eggheadcafe.com/software/aspnet/31021839/normdistxmeanstandarddevtrueinsql2005.aspx DATE: 2010/07/13 PURPOSE: Mimics Excel's Function NORMDIST
Usage: SELECT dbo.udf_NORMDIST(.48321740,0,1,0) OUTPUT: 0.35498205
REVISION HISTORY
Date Developer Details 2010/08/11 LC Posted Function
*****************************************************************************************/
BEGIN
DECLARE @x FLOAT DECLARE @z FLOAT DECLARE @t FLOAT DECLARE @ans FLOAT DECLARE @returnvalue FLOAT
SELECT @x = (@value@mean)/@sigma
IF (@cummulative = 1) BEGIN
SELECT @z = abs(@x)/sqrt(2.0) SELECT @t = 1.0/(1.0+0.5*@z) SELECT @ans = @t*exp(@z*@z1.26551223+@t*(1.00002368+@t*(0.37409196+@t*(0.09678418+@t*(0.18628806+@t*(0.27886807+@t*(1.13520398+@t*(1.48851587+@t*(0.82215223+@t*0.17087277)))))))))/2.0
IF (@x <= 0) SELECT @returnvalue = @ans ELSE SELECT @returnvalue = 1@ans END ELSE BEGIN SELECT @returnvalue = exp(@x*@x/2.0)/sqrt(2.0*3.14159265358979) END
RETURN CAST(@returnvalue AS NUMERIC(28,8))
END




Forum Newbie
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Out of the box there is no equivalent in SQL Server (up to 2012) for NORMDIST.
NORMDIST computes the Normal Distribution PDF (Probability Density Function) when the cumulative parameter is false and the CDF (Cumulative Distribution Function) otherwise.
The PDF can be computed from the definition and is pretty straight forward, the CDF however has no close form and can only be approximated. I've developed a function for the PDF and a set of functions using different approximations for the CDF. You can read my analysis in: http://formaldev.blogspot.com.au/2012/09/TSQLNORMDIST1.html and either copy paste the ones you want from the posts or get them from the project page for the blog posts at: https://tsqlnormdist.codeplex.com/




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I have been able to use the udf_NORMDIST code to stand in for Excel NORM.DIST (NORMDIST). Thankyou very much for posting it!
The other reference from idea/Forum Newbie points to code for NORM.S.DIST (NORMSDIST in older Excel), it seems to be incorrectly labelled as an equivalent for NORMDIST.
However the value returned when @cummulative is set to false (0) seems to be incorrect with some larger numbers, at least it doesn't line up with Excel.
e.g. I used SELECT dbo.udf_NORMDIST(358, 352.791176470588, 234.354144866830, 0) Excel gives me 0.001701885, but this function gave me 0.398843752
So I created a replacement for the line that returns a value when not using cumulative
The formula for this change comes from http://stattrek.com/onlinecalculator/normal.aspx
Normal equation:
The value of the random variable Y is: Y = { 1/[ σ * sqrt(2π) ] } * e(x  μ)2/2σ2
where X is a normal random variable, μ is the mean, σ is the standard deviation, π is approximately 3.14159, and e is approximately 2.71828.
Code change:  Incorrect for larger numbers? SELECT @returnvalue = exp(@x*@x/2.0)/sqrt(2.0*3.14159265358979)  Correct for any numbers... SELECT @returnvalue = (1/(@sigma * sqrt(2.0*3.14159265358979))) * exp(((@value  @mean)*(@value  @mean))/(2*(@sigma*@sigma)))
Also, the precision is not quite right, it needs to be 29,9, not 28,8
Here is a replacement for the function:
CREATE FUNCTION [dbo].[udf_NORMDIST]( @value FLOAT, @mean FLOAT, @sigma FLOAT, @cummulative BIT ) RETURNS NUMERIC( 29,9 ) AS
/**************************************************************************************** NAME: udf_NORMDIST WRITTEN BY: Tim Pickering http://www.eggheadcafe.com/software/aspnet/31021839/normdistxmeanstandarddevtrueinsql2005.aspx DATE: 2010/07/13 PURPOSE: Mimics Excel's Function NORMDIST
Usage: SELECT dbo.udf_NORMDIST(.48321740,0,1,0) OUTPUT: 0.35498205
REVISION HISTORY
Date Developer Details 2010/08/11 LC Posted Function *****************************************************************************************/ BEGIN DECLARE @x FLOAT; DECLARE @z FLOAT; DECLARE @t FLOAT; DECLARE @ans FLOAT; DECLARE @returnvalue FLOAT; SELECT @x = (@value  @mean) / @sigma; IF(@cummulative = 1) BEGIN SELECT @z = ABS( @x ) / SQRT( 2.0 ); SELECT @t = 1.0 / (1.0 + 0.5 * @z); SELECT @ans = @t*exp(@z*@z1.26551223+@t*(1.00002368+@t*(0.37409196+@t*(0.09678418+@t*(0.18628806+@t*(0.27886807+@t*(1.13520398+@t*(1.48851587+@t*(0.82215223+@t*0.17087277)))))))))/2.0; IF(@x <= 0) SELECT @returnvalue = @ans; ELSE SELECT @returnvalue = 1  @ans; END; ELSE BEGIN SELECT @returnvalue = (1/(@sigma * SQRT( 2.0 * 3.14159265358979 ))) * EXP(((@value@mean)*(@value@mean)) / (2*(@sigma*@sigma))); END; RETURN CAST( @returnvalue AS NUMERIC( 29,9 )); END;



