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XLeratorDB/math Documentation

SQL Server radom gamma distribution


RANDGAMMA

Updated: 31 March 2014


Use the table-valued function RANDGAMMA to generate a sequence of random numbers from a gamma distribution with parameters @Shape and @Scale.
Syntax
SELECT * FROM [wctMath].[wct].[RANDGAMMA](
  <@Rows, int,>
 ,<@Shape, float,>
 ,<@Scale, float,>)
Arguments
@Rows
the number of rows to generate. @Rows must be of the type int or of a type that implicitly converts to int.
@Shape
the shape parameter. @Shape must be of the type float or of a type that implicitly converts to float.
@Scale
the scale parameter. @Scale must be of the type float or of a type that implicitly converts to float.
Return Types
RETURNS TABLE (
      [Seq] [int] NULL,
      [X] [float] NULL
)
Remarks
·         @Shape must be greater than zero.
·         @Scale must be greater than zero.
·         If @Shape is NULL then @Shape is set to 1.
·         If @Scale is NULL then @Scale is set to 1.
·         If @Rows is less than 1 then no rows are returned.
Examples
In this example we create a sequence 1,000,000 random numbers rounded to one decimal place from a gamma distribution with @Shape = 9 and @Scale = 0, COUNT the results, paste them into Excel, and graph them.
SELECT
   X,
   COUNT(*) as [COUNT]
FROM (
   SELECT
      ROUND(X,1) as X
   FROM
      wct.RANDGAMMA(
         1000000, --@Rows
         9,       --@Shape
         0.5      --@Scale
         )
   )n
GROUP BY
   X
ORDER BY
   X

This produces the following result.


In this example we generate 1,000,000 random numbers from a gamma distribution with @Shape of 5 and @Scale of 2. We calculate the mean, standard deviation, skewness, and excess kurtosis from the resultant table and compare those values to the expected values for the distribution.
DECLARE @size as int = 1000000
DECLARE @Shape as float = 5
DECLARE @scale as float = 2
DECLARE @mean as float = @Shape*@Scale
DECLARE @var as float = @Shape*POWER(@Scale,2)
DECLARE @stdev as float = SQRT(@var)
DECLARE @skew as float = 2/SQRT(@Shape)
DECLARE @kurt as float = 6e+00/@Shape
 
SELECT
   stat,
   [RANDGAMMA],
   [EXPECTED]
FROM (
   SELECT
      x.*
   FROM (
      SELECT
          MIN(x) as min_GAMMA
         ,AVG(x) as mean_GAMMA
         ,MAX(x) as max_GAMMA
         ,STDEVP(x) as stdev_GAMMA
         ,wct.SKEWNESS_P(x) as skew_GAMMA
         ,wct.KURTOSIS_P(x) as kurt_GAMMA
      FROM
         wct.RANDGAMMA(@size,@Shape,@scale)
      )n
   CROSS APPLY(
      VALUES
         ('RANDGAMMA','avg', mean_GAMMA),
         ('RANDGAMMA','stdev', stdev_GAMMA),
         ('RANDGAMMA','skew', skew_GAMMA),
         ('RANDGAMMA','kurt', kurt_GAMMA),
         ('EXPECTED','avg',@mean),
         ('EXPECTED','stdev',@stdev),
         ('EXPECTED','skew',@skew),
         ('EXPECTED','kurt',@kurt)
      )x(fn_name,stat,val_stat)    
   )d
PIVOT(sum(val_stat) FOR fn_name in([RANDGAMMA],[EXPECTED])) P

This produces the following result (your result will be different).

stat
RANDGAMMA
EXPECTED
avg
9.998933155
10
kurt
1.21987376
1.2
skew
0.896956119
0.894427191
stdev
4.473389818
4.472135955

 

See Also

 



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