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XLeratorDB/windowing Documentation

SQL Server moving sample KURTOSIS function


MovingKURT_S

Updated: 30 Jun 2013


Use MovingKURT_S to calculate the sample kurtosis of column values in an ordered resultant table, without the need for a self-join. The sample kurtosis is calculated for each value from the first value in the window to the last value in the window. If the column values are presented to the functions out of order, an error message will be generated.
Syntax
SELECT [westclintech].[wct].[MovingKURT_S](
  <@Val, float,>
 ,<@Offset, int,>
 ,<@RowNum, int,>
 ,<@Id, tinyint,>
 ,<@Exact, bit,>)
Arguments
@Val
the value passed into the function. @Val is an expression of type float or of a type that can be implicitly converted to float.
@Offset           
specifies the window size. @Offset is an expression of type int or of a type that can be implicitly converted to int.
@RowNum
the number of the row within the group for which the sample kurtosis is being calculated. If @RowNum for the current row in a set is less than or equal to the previous @RowNum and @RowNum is not equal to 1, an error message will be generated. @RowNum is an expression of type int or of a type that can be implicitly converted to int.
@Id
a unique identifier for the MovingKURT_S calculation. @Id allows you to specify multiple moving sample kurtosis calculations within a resultant table. @Id is an expression of type tinyint or of a type that can be implicitly converted to tinyint.
@Exact
a bit value which tells the function whether or not to return a NULL value if the number of rows in the window is smaller the @Offset value. If @Exact is 'True' and the number of rows in the window is less the @Offset then a NULL is returned. @Exact is an expression of type bit or of a type that can be implicitly converted to bit.
Remarks
·         If @Id is NULL then @Id = 0.
·         To calculate the sample kurtosis from the beginning of a dataset or a partition, use the RunningKURT_S function.
·         To calculate the sample kurtosis for an entire data set or for an entire group within a data set use the KURTOSIS_S function.
·         If @RowNum is equal to 1, MovingKURT_S is equal to zero
·         @RowNum must be in ascending order.
·         If @Exact IS NULL then @Exact = 'True'
·         There may be cases where the order in which the data are returned to the function and the order in which the results are returned are different, generally due to parallelism. You can use OPTION(MAXDOP 1) or OPTION(MAXDOP 1,FORCE ORDER) to help eliminate this problem.
Example
In this example, we have 20 rows of data and we want to caculate the sample kurtosis of x and y over a window of 10 rows. Note that the @Id value for each MovingKURT_S column is different. Since @Exact is NULL, NULL is returned when the window size is less than @Offset.
SELECT rn
,x
,y
,wct.MovingKURT_S(x,10,ROW_NUMBER() OVER (ORDER BY RN), NULL, NULL) as [KURT_S x]
,wct.MovingKURT_S(y,10,ROW_NUMBER() OVER (ORDER BY RN), 1, NULL) as [KURT_S y]
FROM (
      SELECT 1,101,117 UNION ALL
      SELECT 2,91,97 UNION ALL
      SELECT 3,96,121 UNION ALL
      SELECT 4,96,103 UNION ALL
      SELECT 5,86,74 UNION ALL
      SELECT 6,95,80 UNION ALL
      SELECT 7,91,105 UNION ALL
      SELECT 8,102,72 UNION ALL
      SELECT 9,94,108 UNION ALL
      SELECT 10,110,94 UNION ALL
      SELECT 11,121,85 UNION ALL
      SELECT 12,115,90 UNION ALL
      SELECT 13,112,96 UNION ALL
      SELECT 14,100,97 UNION ALL
      SELECT 15,124,106 UNION ALL
      SELECT 16,92,61 UNION ALL
      SELECT 17,92,107 UNION ALL
      SELECT 18,139,92 UNION ALL
      SELECT 19,95,101 UNION ALL
      SELECT 20,90,104
      )n(rn,x,y)
This produces the following result.
         rn           x           y               KURT_S x               KURT_S y
----------- ----------- ----------- ---------------------- ----------------------
          1         101         117                   NULL                   NULL
          2          91          97                   NULL                   NULL
          3          96         121                   NULL                   NULL
          4          96         103                   NULL                   NULL
          5          86          74                   NULL                   NULL
          6          95          80                   NULL                   NULL
          7          91         105                   NULL                   NULL
          8         102          72                   NULL                   NULL
          9          94         108                   NULL                   NULL
         10         110          94      0.903518395517902      -1.14057778810637
         11         121          85       1.71183831181016     -0.882927402614166
         12         115          90     -0.482900842240177     -0.833857539549565
         13         112          96      -1.27304409446808      -1.31748255215644
         14         100          97      -1.16396843287532      -1.05288910685806
         15         124         106      -1.41893917091015      -0.54028716568535
         16          92          61      -1.46520920354463      0.394440723606388
         17          92         107      -1.47713918669122      0.313881909458232
         18         139          92     -0.467222315103836       3.11868316976853
         19          95         101     -0.430584490740741       3.82118179140153
         20          90         104     -0.750956632653061       3.58241892176539
 


This example uses the same data as the previous example, however @Exact has been set to
'FALSE'.
SELECT rn
,x
,y
,wct.MovingKURT_S(x,10,ROW_NUMBER() OVER (ORDER BY RN), NULL, 'FALSE') as [KURT_S x]
,wct.MovingKURT_S(y,10,ROW_NUMBER() OVER (ORDER BY RN), 1, 'FALSE') as [KURT_S y]
FROM (
      SELECT 1,101,117 UNION ALL
      SELECT 2,91,97 UNION ALL
      SELECT 3,96,121 UNION ALL
      SELECT 4,96,103 UNION ALL
      SELECT 5,86,74 UNION ALL
      SELECT 6,95,80 UNION ALL
      SELECT 7,91,105 UNION ALL
      SELECT 8,102,72 UNION ALL
      SELECT 9,94,108 UNION ALL
      SELECT 10,110,94 UNION ALL
      SELECT 11,121,85 UNION ALL
      SELECT 12,115,90 UNION ALL
      SELECT 13,112,96 UNION ALL
      SELECT 14,100,97 UNION ALL
      SELECT 15,124,106 UNION ALL
      SELECT 16,92,61 UNION ALL
      SELECT 17,92,107 UNION ALL
      SELECT 18,139,92 UNION ALL
      SELECT 19,95,101 UNION ALL
      SELECT 20,90,104
      )n(rn,x,y)
This produces the following result.
         rn           x           y               KURT_S x               KURT_S y
----------- ----------- ----------- ---------------------- ----------------------
          1         101         117                   NULL                   NULL
          2          91          97                   NULL                   NULL
          3          96         121                   NULL                   NULL
          4          96         103                    1.5      -4.11489694128959
          5          86          74     -0.177514792899409       0.38921288454255
          6          95          80      0.653089374822511      -1.70637468912197
          7          91         105      0.238796694436977      -1.07718583354361
          8         102          72     -0.446379105658885      -1.63506342871445
          9          94         108    -0.0668571428571427      -1.40746937458679
         10         110          94      0.903518395517902      -1.14057778810637
         11         121          85       1.71183831181016     -0.882927402614166
         12         115          90     -0.482900842240177     -0.833857539549565
         13         112          96      -1.27304409446808      -1.31748255215644
         14         100          97      -1.16396843287532      -1.05288910685806
         15         124         106      -1.41893917091015      -0.54028716568535
         16          92          61      -1.46520920354463      0.394440723606388
         17          92         107      -1.47713918669122      0.313881909458232
         18         139          92     -0.467222315103836       3.11868316976853
         19          95         101     -0.430584490740741       3.82118179140153
         20          90         104     -0.750956632653061       3.58241892176539
 


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