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XLeratorDB/windowing Documentation

SQL Server running sample SKEW function


RunningSKEW_S

Updated: 30 June 2013


Use RunningSKEW_S to calculate the samples skewness of column values in an ordered resultant table, without the need for a self-join. The sample skewness 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].[RunningSKEW_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 skewness 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 RunningSKEW_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 skewness, use the MovingSKEW_S function.
·         To calculate the samples skewness for an entire data set, use the SKEWNESS_S function.
·         If @RowNum is equal to 1, RunningSKEW_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 skewness of x and y starting from the first row. Note that the @Id value for each RunningSKEW_S column is different.
SELECT rn
,x
,y
,wct.RunningSKEW_S(x,rn,NULL) as [SKEW_S x]
,wct.RunningSKEW_S(y,rn,1) as [SKEW_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               SKEW_S x               SKEW_S y
---- ----------- ----------- ---------------------- ----------------------
   1         101         117                   NULL                   NULL
   2          91          97                   NULL                   NULL
   3          96         121                      0      -1.54539252569502
   4          96         103                      0     -0.129678815660363
   5          86          74     -0.404796008910937     -0.864550209720427
   6          95          80     -0.547871643589439     -0.179587851309796
   7          91         105     -0.179812666650057     -0.384309637141166
   8         102          72     -0.183091963166347    -0.0994544316100886
   9          94         108     -0.124285714285715     -0.331171026292888
  10         110          94      0.709070384461684     -0.265262411674906
  11         121          85        1.2958445379977    -0.0584746272003931
  12         115          90      0.893378681947106     0.0476461160613627
  13         112          96      0.618377295780968     0.0401051990837308
  14         100          97      0.653762183949444     0.0164309317695287
  15         124         106      0.625574752271121     -0.119264289357361
  16          92          61      0.731016831476697     -0.359228636579172
  17          92         107      0.828122509715119      -0.47105159705444
  18         139          92       1.16094637809343     -0.446870439048321
  19          95         101       1.24572587647292     -0.518472653357385
  20          90         104       1.30010690278267     -0.602170891442928
 


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