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XLeratorDB/statistics Documentation

SQL Server T.DIST function


T_DIST

Updated: 31 July 2015

Use T_DIST to calculate the probability density function and the left-tailed cumulative probability distribution of Student's t-distribution.
Syntax
SELECT [wct].[T_DIST](
  <@X, float,>
 ,<@df, float,>
 ,<@Cumulative, bit,>)
Arguments
@X
the value of interest to be evaluated. @X must be of a type float or of type that intrinsically converts to float
@df
the number of degrees of freedom. @df must of a type float or of a type that intrinsically converts to float.
@Cumulative
A bit value indicating whether the probability density function ('False') or the cumulative distribution function ('True') should be returned.
Return Type
float
Remarks
·         0 < @df
Examples
In this example we calculate the probability density function for x = 8 with 3 degrees of freedom.
SELECT
       wct.T_DIST(
               8            --@X
              ,3            --@df
              ,'False'      --@Cumulative       
              ) as pdf

This produces the following result
 


In this example we calculate the left-tailed cumulative distribution function for x = 60 with 1 degree of freedom.
SELECT
       wct.T_DIST(
               60                  --@X
              ,1                   --@df
              ,'True'              --@Cumulative       
              ) as cdf

This produces the following result.
 


The left-tailed cumulative distribution is closely related to the beta distribution.
SELECT
        wct.T_DIST(x,df,'True') as T_DIST
       ,(1-wct.BETA_DIST(x*x/(df+x*X),0.5,df*0.5,'True',NULL,NULL))*0.5 as BETA_DIST
FROM (VALUES(-2e-00,5e-00))n(x,df)

This produces the following result.

 

See Also

 



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