Login     Register

        Contact Us     Search

XLeratorDB/math Documentation

SQL Server random t-distribution


RANDTDIST

Updated: 31 March 2014


Use the table-valued function RANDTDIST to generate a sequence of random numbers from Student's t distribution with parameter @df.
Syntax
SELECT * FROM [wctMath].[wct].[RANDTDIST](
  <@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 @Shape 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 Student's t distribution with @df = 10, COUNT the results, paste the results into Excel and graph them.
SELECT
   X,
   COUNT(*) as [COUNT]
FROM (
   SELECT
      ROUND(X,1) as X
   FROM
      wct.RANDTDIST(
         1000000, --@Rows
         10       --@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 t distribution with @lambda of 6. 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 @lambda as float = 6
DECLARE @mean as float = 0
DECLARE @var as float =
CASE
WHEN @lambda <= 2 THEN NULL
ELSE @lambda /(@lambda -2)
END
DECLARE @stdev as float = SQRT(@var)
DECLARE @skew as float = 0
DECLARE @kurt as float =
CASE
WHEN @lambda <= 4 THEN NULL
ELSE 6/(@lambda -4)
END
 
SELECT
   stat,
   [RANDTDIST],
   [EXPECTED]
FROM (
   SELECT
      x.*
   FROM (
      SELECT
         AVG(x) as mean_TDIST,
         STDEVP(x) as stdev_TDIST,
         wct.SKEWNESS_P(x) as skew_TDIST,
         wct.KURTOSIS_P(x) as kurt_TDIST
      FROM
         wct.RANDTDIST(@size, @lambda)
      )n
   CROSS APPLY(
      VALUES
         ('RANDTDIST','avg', mean_TDIST),
         ('RANDTDIST','stdev', stdev_TDIST),
         ('RANDTDIST','skew', skew_TDIST),
         ('RANDTDIST','kurt', kurt_TDIST),
         ('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([RANDTDIST],[EXPECTED])) P

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

stat
RANDTDIST
EXPECTED
avg
-0.003034901
0
kurt
3.090949021
3
skew
0.023943502
0
stdev
1.224957684
1.224744871

 

See Also

 



Copyright 2008-2013 WestClinTech LLC         Privacy Policy        Terms of Service