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Is there an equivalent of Excel's NORMDIST...
Is there an equivalent of Excel's NORMDIST function in SQL Server 2005?
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L Cerniglia
L Cerniglia
Posted Monday, August 9, 2010 7:55 AM
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Group: General Forum Members
Last Login: Tuesday, January 13, 2015 11:40 AM
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Is there an equivalent of Excel's NORMDIST function in SQL Server 2005?
Post #965963
Sean Lange
Sean Lange
Posted Monday, August 9, 2010 9:01 AM
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Last Login: Tuesday, December 6, 2016 8:08 PM
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Nothing right out of the box that i know of. You will probably have to write your own. (or borrow somebody else's)
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Post #966025
L Cerniglia
L Cerniglia
Posted Friday, August 13, 2010 6:31 AM
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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
Post #968851
idea
idea
Posted Wednesday, September 12, 2012 8:15 PM
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Group: General Forum Members
Last Login: Wednesday, September 12, 2012 8:45 PM
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Visits: 4
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/
Post #1358295
chris.palmer.nz
chris.palmer.nz
Posted Tuesday, May 5, 2015 6:15 PM
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Group: General Forum Members
Last Login: Monday, December 5, 2016 3:58 PM
Points: 2,
Visits: 85
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;
Post #1682972
dwain.c
dwain.c
Posted Tuesday, May 19, 2015 9:35 PM
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Group: General Forum Members
Last Login: Wednesday, February 24, 2016 6:28 AM
Points: 3,977,
Visits: 6,431
Nothing out of the box as stated, but there is this:
Excel in TSQL Part 2 – The Normal Distribution (NORM.DIST) Density Functions
There are also some links at the end to approximation formulas for the cumulative distribution function. The probability density function is pretty straightforward.
My mantra:
No loops! No CURSORs! No RBAR! Hoouh!
My thought question:
Have you ever been told that your query runs too fast?
My advice:
INDEXing a poorperforming query is like putting sugar on cat food. Yeah, it probably tastes better but are you sure you want to eat it?
The path of least resistance can be a slippery slope. Take care that fixing your fixes of fixes doesn't snowball and end up costing you more than fixing the root cause would have in the first place.
Need to UNPIVOT? Why not CROSS APPLY VALUES instead?
Since random numbers are too important to be left to chance, let's generate some!
Learn to understand recursive CTEs by example.
Splitting strings based on patterns can be fast!
My temporal SQL musings:
Calendar Tables
,
an Easter SQL
,
Time Slots
and
Selfmaintaining, Contiguous Effective Dates in Temporal Tables
Post #1687103
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