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XLeratorDB/math Documentation

SQL Server random chi-squared distribution


RANDCHISQ

Updated: 31 March 2014


Use the table-valued function RANDCHISQ to generate a sequence of random numbers from a chi-squared distribution with @df degrees of freedom.
Syntax
SELECT * FROM [wctMath].[wct].[RANDCHISQ](
  <@Rows, int,>
 ,<@df, 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.
@df
the degrees of freedom. @df 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
·         @df must be greater than zero.
·         If @df is NULL then @df is set to 1.
·         If @MaxIterations 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 chi-squared distribution with @df = 1, COUNT the results, paste them into Excel and graph them.
SELECT
   X,
   COUNT(*) as [COUNT]
FROM (
   SELECT
      ROUND(X,1) as X
   FROM
      wct.RANDCHISQ(
         1000000, --@Rows
         1     --@df
      )
   )n
GROUP BY
   X
ORDER BY
   X

This produces the following result.


In this example we generate 1,000,000 random numbers from a chi-squared distribution with @df of 9. 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 @df as float = 9
DECLARE @mean as float = @df
DECLARE @var as float = 2*@df
DECLARE @stdev as float = SQRT(@var)
DECLARE @skew as float = SQRT(8e+00/@df)
DECLARE @kurt as float = 12e+00/@df
 
SELECT
   stat,
   [RANDCHISQ],
   [EXPECTED]
FROM (
   SELECT
      x.*
   FROM (
      SELECT
         AVG(x) as mean_CHISQ,
         STDEVP(x) as stdev_CHISQ,
         wct.SKEWNESS_P(x) as skew_CHISQ,
         wct.KURTOSIS_P(x) as kurt_CHISQ
      FROM
         wct.RANDCHISQ(@size,@df)
      )n
   CROSS APPLY(
      VALUES
         ('RANDCHISQ','avg', mean_CHISQ),
         ('RANDCHISQ','stdev', stdev_CHISQ),
         ('RANDCHISQ','skew', skew_CHISQ),
         ('RANDCHISQ','kurt', kurt_CHISQ),
         ('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([RANDCHISQ],[EXPECTED])) P

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

stat
RANDCHISQ
EXPECTED
avg
8.996961719
9
kurt
1.343216314
1.333333333
skew
0.944388767
0.942809042
stdev
4.23988631
4.242640687

 

See Also

 



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