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XLeratorDB/statistics Documentation

SQL Server sample skewness function


SKEWNESS_S

Updated: 24 May 2013


Use the aggregate function SKEWNESS_S to calculate the sample skewness. The SKEWNESS_S function is an implementation of the EXCEL SKEW function. The formula for SKEWNESS_S is:

XLeratorDB formula for Sample Skewness (SKEWNESS.S) for SQL Server
Syntax
XLeratorDB syntax for Sample Skewness function (SKEWNESS.S) for SQL Server
Arguments
@Known_x
the values to be used in the calculation. @Known_x must be of a type float or of a type that implicitly converts to float.
Return Types
float
Remarks
·         If you want measure the skewness for a population, then use the SKEWNESS_P function.
·         To calculate the population kurtosis use the KURTOSIS_P function.
·         To calculate the sample kurtosis use the KURTOSIS_S function.
Examples
SELECT wct.SKEWNESS_S(x) as SKEWNESS_S
FROM (
      SELECT 30000.0000216303 UNION ALL
      SELECT 30000.0000565854 UNION ALL
      SELECT 30000.000038137 UNION ALL
      SELECT 30000.0000495983 UNION ALL
      SELECT 30000.0000185861 UNION ALL
      SELECT 30000.0000863479 UNION ALL
      SELECT 30000.0000776366 UNION ALL
      SELECT 30000.0000637985 UNION ALL
      SELECT 30000.0000939786 UNION ALL
      SELECT 30000.000031191 UNION ALL
      SELECT 30000.0000550457 UNION ALL
      SELECT 30000.0000207558 UNION ALL
      SELECT 30000.0000805531 UNION ALL
      SELECT 30000.0000241287
      )n(x)
 
This produces the following result
            SKEWNESS_S
----------------------
     0.229491026413433

In this example, we generate 100 random numbers form the standard normal distribution using the wct.SeriesFloat function and calculate the sample skewness.
SELECT wct.SKEWNESS_S(k.SeriesValue) as SKEWNESS_S
FROM wctMath.wct.SeriesFloat(0,1,NULL,100,'N')k
This produces the following result (your results will be different).
            SKEWNESS_S
----------------------
    -0.153829198515644
 


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