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XLeratorDB/windowing Documentation

SQL Server running sample KURTOSIS function


RunningKURT_S

Updated: 30 June 2013


Use RunningKURT_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 over all the values from the first value to the last value in the ordered group or partition. If the column values are presented to the functions out of order, an error message will be generated.
Syntax
SELECT [westclintech].[wct].[RunningKURT_S](
  <@X, float,>
 ,<@RowNum, int,>
 ,<@Id, tinyint,>)
Arguments
@X
the value passed into the function. @X is an expression of type float or of a type that can be implicitly converted to float.
@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 RunningKURT_S calculation. @Id allows you to specify multiple running sample skewness calculations within a resultant table. @Id is an expression of type tinyint or of a type that can be implicitly converted to tinyint.
Remarks
·         If @Id is NULL then @Id = 0.
·         To calculate moving sample kurtosis, use the MovingKURT_S function.
·         To calculate the sample kurtosis for an entire data set, use the KURTOSIS_S function.
·         If @RowNum is equal to 1, RunningKURT_S is equal to zero.
·         @RowNum must be in ascending order.
·         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 starting from the first row. Note that the @Id value for each RunningKURT_S column is different.
SELECT rn
,x
,y
,wct.RunningKURT_S(x,rn,NULL) as [KURT_S x]
,wct.RunningKURT_S(y,rn,1) 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      0.389212884542543
   6          95          80      0.653089374822509      -1.70637468912197
   7          91         105      0.238796694436977      -1.07718583354361
   8         102          72     -0.446379105658887      -1.63506342871445
   9          94         108    -0.0668571428571463      -1.40746937458679
  10         110          94        0.9035183955179      -1.14057778810637
  11         121          85       1.80974330712932      -1.17954713149457
  12         115          90   -0.00554937100889941     -0.997578017618969
  13         112          96       -0.6802006038621     -0.767217614514457
  14         100          97      -0.44238457089804     -0.554922326554543
  15         124         106     -0.685738954145421      -0.53957325173014
  16          92          61      -0.56349975591933      -0.31799220337797
  17          92         107     -0.419582246269193     -0.255917838308746
  18         139          92      0.854487881313605     -0.115157025183854
  19          95         101       1.09029070734079     0.0477693152924239
  20          90         104       1.22585595223078      0.175899602607029
 


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