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XLeratorDB/statistics Documentation

SQL Server T.DIST function


TPDF

Updated: 31 July 2010


Use TPDF to calculate the probability density function of the T distribution.
 
The formula for the probability density function is:

formula for sql server analytic function TPDF
 
Where
                x              the t-statistic
                v             the degrees of freedom
                B             the Beta function
Syntax
SELECT [wctStatistics].[wct].[TPDF] (
  <@X, float,>
 ,<@Degrees_freedom, float,>)
Arguments
@X
the variable to be evaluated. @X is an expression of type float or of a type that implicitly converts to float
@Degrees_Freedom
is the degrees of freedom. @Degrees_Freedom is an expression of type float or of a type that implicitly converts to float
Return Types
float
Remarks
·         @Degrees_Freedom must be greater than zero (@DF > 0).
Examples
Calculate the probability density function:
SELECT wct.TPDF(1,3) as [T pdf]
This produces the following result
                 T pdf
----------------------
     0.206748335783172
 
You can use the SeriesFloat function from the XLeratorDB/math module to generate a dataset which can be pasted into EXCEL to generate a graph of the probability density function.
SELECT SeriesValue
,wct.NCTPDF(SeriesValue, 1, 1) as [f(x,1,1)]
,wct.NCTPDF(SeriesValue, 3, 1) as [f(x,3,1)]
,wct.NCTPDF(SeriesValue, 5, 1) as [f(x,5,1)]
,wct.NCTPDF(SeriesValue, 1, 3) as [f(x,1,3)]
,wct.NCTPDF(SeriesValue, 1, 5) as [f(x,1,5)]
FROM wctMath.wct.SeriesFloat(.1, 10, .1,NULL,NULL)
This is an EXCEL-generated graph of the results

 
 


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