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XLeratorDB/windowing Documentation

SQL Server running population SKEW function


RunningSKEW_P

Updated: 30 June 2013


Use RunningSKEW_P to calculate the population skewness of column values in an ordered resultant table, without the need for a self-join. The population 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_P](
  <@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 population 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_P calculation. @Id allows you to specify multiple moving population 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 population skewness, use the MovingSKEW_P function.
·         To calculate the population skewness for an entire data set, use the SKEWNESS_P function.
·         If @RowNum is equal to 1, RunningSKEW_P 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 population skewness of x and y starting from the first row. Note that the @Id value for each RunningSKEW_P column is different.
SELECT rn
,x
,y
,wct.RunningSKEW_P(x,rn,NULL) as [SKEW_P x]
,wct.RunningSKEW_P(y,rn,1) as [SKEW_P 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_P x               SKEW_P y
---- ----------- ----------- ---------------------- ----------------------
   1         101         117                   NULL                   NULL
   2          91          97                   NULL                   NULL
   3          96         121                      0     -0.630903856710624
   4          96         103                      0    -0.0748700991297024
   5          86          74     -0.271545417883639     -0.579957911668972
   6          95          80     -0.400108877081822     -0.131152422955012
   7          91         105     -0.138728484148604     -0.296501322167989
   8         102          72     -0.146800156380065    -0.0797409447174197
   9          94         108      -0.10253048327205     -0.273202158161578
  10         110          94       0.59794064967205     -0.223688906272518
  11         121          85       1.11198535961314    -0.0501780325100918
  12         115          90      0.777586334170716     0.0414706209967757
  13         112          96      0.544607881006138      0.035320843179948
  14         100          97      0.581520926533674      0.014615300335522
  15         124         106      0.561193868737353     -0.106990232108443
  16          92          61      0.660617069958198      -0.32463352295545
  17          92         107      0.753184539376549     -0.428425475684856
  18         139          92        1.0618701934365     -0.408734122873594
  19          95         101       1.14513939145121     -0.476608433655409
  20          90         104       1.20049338388635     -0.556032868988637
 


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