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XLeratorDB/statistics Documentation

SQL Server incomplete beta function


 
Updated: 9 August 2010

Use BETAI to calculate the incomplete beta function. The incomplete beta function is defined by:
 BETAI
Syntax
SELECT [wctStatistics].[wct].[BETAI] (
   <@A, float,>
 ,<@B, float,>
 ,<@X, float,>)
Arguments
@A
is any real number greater than or equal to zero. @A is an expression of type float or of a type that can be implicitly converted to float@A is the lower bound to the distribution. If you enter NULL, @A defaults to zero
@B
is any real number greater than or equal to zero. @B is an expression of type float or of a type that can be implicitly converted to float.   @B is the upper bound to the distribution. If you enter NULL @B defaults to to zero.
@X
is any real number greater than or equal to zero and less than or equal to one. @X is an expression of type float or of a type that can be implicitly converted to float
Return Types
float
Remarks
·         If @A ≤ 0 or @B ≤ 0, BETAI returns an error.
·         If @X < 0 or @X > 1, BETAI returns an error.
·         @X = 0 or @X = 1, BETAI = @X
·         BETAI(@A, @B, @X) = BETADIST(@X, @A, @B, 0, 1)
Examples

select
wct.BETAI(1, 5, .45)

This produces the following result

----------------------
0.9496715625
 
(1 row(s) affected)
 
select wct.BETADIST(.45,1,5,0,1)

This produces the following result

----------------------
0.9496715625
 
(1 row(s) affected)


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